Research Article An Occupancy Based Cyber-Physical...

Research ArticleAn Occupancy Based Cyber-Physical System Design forIntelligent Building Automation

Kottarathil Eashy Mary Reena1 Abraham Theckethil Mathew1 and Lillykutty Jacob2

1Department of EE National Institute of Technology Calicut India2Department of ECE National Institute of Technology Calicut India

Correspondence should be addressed to Kottarathil Eashy Mary Reena maryreenakegmailcom

Received 3 April 2015 Revised 31 July 2015 Accepted 9 August 2015

Academic Editor Yong Lei

Copyright copy 2015 Kottarathil Eashy Mary Reena et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Cyber-physical system (CPS) includes the class of Intelligent Building Automation System (IBAS) which increasingly utilizesadvanced technologies for long term stability economy longevity and user comfort However there are diverse issues associatedwith wireless interconnection of the sensors controllers and power consuming physical end devices In this paper a novelarchitecture of CPS for wireless networked IBAS with priority-based access mechanism is proposed for zones in a large buildingwith dynamically varying occupancy Priority status of zones based on occupancy is determined using fuzzy inference engineNondominated Sorting Genetic Algorithm-II (NSGA-II) is used to solve the optimization problem involving conflicting demandsof minimizing total energy consumption andmaximizing occupant comfort levels in building An algorithm is proposed for powerscheduling in sensor nodes to reduce their energy consumption Wi-Fi with Elimination-Yield Nonpreemptive Multiple Access(EY-NPMA) scheme is used for assigning priority among nodes for wireless channel access Controller design techniques are alsoproposed for ensuring the stability of the closed loop control of IBAS in the presence of packet dropouts due to unreliable networklinks

1 Introduction

Cyber-physical systems (CPSs) are the system level integra-tions of the computation networking andphysical dynamicsin which embedded devices such as sensors and actuatorsare (wirelessly) networked to sense monitor and con-trol the physical world [1] CPSs are expected to have atremendous impact on many critical sectors (such as energymanufacturing healthcare transportation and aerospace)of the economy and they transform the way human-to-human human-to-object and object-to-object interactionstake place in the physical and virtual worlds [2] Complexcyber-physical systems are compositions of heterogeneouscomponents they often include thermal electromechanicalchemical computing and communication elements withan underlying data network thread for communication andcontrol The dynamics of all the networked elements bothcyber and physical are critical to the performance of theoverall system [3] In energy conservation application of CPS

in large scale and comfort critical systems like IntelligentBuilding Automation System (IBAS) various physical sys-tems comprise HVAC (heating ventilation and air condi-tioning) lighting elevators and other electrical subsystemson each floor which are networked and controlled to achievethe set goal of energy efficiency user comfort and economicoperation [4]

Further the skyrocketing energy costs and the widelyaccepted concept of green buildings are driving the adop-tion of Networked Control Systems (NCSs) for buildingautomation so as to use the best technology for the pur-poses mentioned above [5 6] NCSs combine low cost andlow power devices with embedded processors networkedin order to provide intelligent and efficient sensing andactuation over a geographic area [7] Energy efficiency andoccupant comfort are two major issues in building controlsystem design as discussed above and research efforts areneeded to develop appropriate communication and controlstrategies for minimizing the total energy consumed without

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 132182 15 pageshttpdxdoiorg1011552015132182

2 Mathematical Problems in Engineering

compromising the indoor comfort Here the problem isformulated as a critical control system so that the economyand longevity are assured by exploiting the advantages ofmodern communication and control technologies

In order to build intelligence in BAS a sensor networkconsisting of hundreds of sensors in a building can accuratelybe deployed to monitormeasure the temperature air qual-ity light humidity door or windowrsquos openclose positionand occupancy accurately [8] Occupancy sensors can beinstalled to automatically switch the HVAC and lighting sys-tem in accordance with the occupancy status of the buildingzones Actuator nodes in turn would have the responsibilityto control the subsystems within the building zones Energysavings can be more when the separate subsystems cooperateand communicate with each other Integration of thesesubsystems would add more sophistication to the controlsystem and it would be possible to render an intelligentsystem of Building Automation System (BAS) Enhancementof battery life of sensor nodes will naturally lead to networkavailability and system reliability

Looking at the cost factor and deployability it is seenthat the necessity of wireless BAS arises in various situations(i) when wiring is expensive and time-consuming (ii) whenit demands scalability and flexibility in the deployment ofsensoractuator nodes and (iii) when there is need forredeployment or retrofit without affecting the aestheticsof existing buildings [9] With due design considerationsand planning and by adopting appropriate implementationtechniques wireless technology can be used economicallyand efficiently The advantages of wireless technology cannotbe outweighed by the challenges like poor channel condi-tions and competition for channel access which may createunreliable and delayed communication of control and datatraffic Hence intense research efforts are needed to addressthe diverse issues in real time control of BAS over wirelessnetworks using open standards rather than proprietarystandards

The scenario of control that has been considered in thiswork is the automation of large shared spaces of commercialbuildings where big crowd occupies the space and movesfrom one space to another Occupancy pattern changesdynamically and unpredictably thus making the controlneeded for comfort and economy difficult otherwise [10]Normally the settings of the building climate control systemare to be in such a way that occupant comfort level is themaximum However this results into wastage of energy forlighting lamps coolingheating space and for air qualityassurance for unoccupied spaces also Moreover energyis wasted for overcooling and for cooling less occupiedspaces In modern approaches the building thermal zonesare divided based on the positioning of variable air volume(VAV) boxes of HVAC [11] The problem considered here isof a large shared space comprising more than one thermalzone of the building Occupancy patterns vary dynamicallyand the zones are classified into different priority classesThe requirement is that comfort level of heavily occupiedldquoprime zonesrdquo shall be maintained maximum compared tothe lightly occupied zones in concurrence with the energysaving in ldquovacantrdquolightly occupied zones In the proposed

method priority is assigned for wireless traffic of prime zonesusing quality of service (QoS) medium access control (MAC)protocol Emphasis is given to the competition among primezonesrsquos sensors belonging to the same shared space Stabilityof the closed loop control over wireless networks has beenensured while packet drops due to unreliable links existAdditionally the energy consumed by the nodes have tobe minimized to provide longer battery life and extendednetwork availability

The proposed architecture has a hierarchical structurefor communication and control and has the following fea-turesfunctionality (i) it decides the status of a particularzone based on its density and rate of change of occupancyand assigns proportional weights to the objective functionsusing fuzzy logic rule base (ii) it offers priority to the networktraffic of prime zones by QoS differentiated medium accesscontrol (MAC) via Elimination-Yield Nonpreemptive Multi-ple Access (EY-NPMA) scheme adopted withWi-Fi protocol(iii) it optimizes energy consumption and user comfort inevery zone based on occupancy using Nondominated SortedGenetic Algorithm-II (NSGA-II) (iv) it schedules transmitpower and sampling rates of wireless sensor nodes throughthe algorithm proposed (v) it deals with design of distributedlocal controllers to guarantee the stability of the closedloop control in presence of packet drops (due to unreliablenetwork links)

The remaining part of the paper is organized as followsa brief review of the related work is given in Section 2Architecture for an energy-efficient priority-access baseddecentralized controller for wireless BAS is described inSection 3 Sections 31ndash35 explain the fuzzy rule base forzone status selection the concept of EY-NPMA schemethe multiobjective optimization problem formulation usingNSGA-II the sensor node power scheduling algorithm forWSN and the decentralized controller design in the sequelSimulation results and discussions are described in Section 4Paper is concluded in Section 5

2 Related Work

21 Wireless Sensor Networks in Intelligent Building Automa-tion There has been an overwhelming interest in the recentpast for using the advanced technology to make the build-ing control more intelligent Wang et al [12] present abuilding energy management system with wireless sensornetworks using multiagent distributed control methodologythat concentrates on optimized target of air conditioninglighting and official electrical devices A multitier systemview point is used to incorporate the various levels of sensingprocessing communication and management functionalityThe cyber-physical building energy management system(CBEMS) has been assumed with a high level of intelligenceand automation The occupant comfort quality level is not aconcern here Authors in [13] describe a simple web servicecalled the Simple Measuring and Actuation Profile (sMAP)which allows instruments and other producers of physicalinformation to directly publish their data in cyber space Self-describing physical information which is uniform and withmachine independent access would avoid the innumerable

Mathematical Problems in Engineering 3

drivers and adapters for specific sensor and actuator devicesfound in industrial building automation process control andenvironmental monitoring solutions

In [14] authors discuss joint problems of control andcommunication in wireless sensor and actuator networks(WSANs) used for closing control loops in building-environment control systems The paper presents a central-ized control (CC) scheme (decisions are made based onglobal information) and a decentralized control (DC) scheme(distributed actuators to make control decisions locally)Inference has been given as DC outperforms CC whentraffic and packet-loss rates are high Mady et al in [15]present a BAS using interactive control strategies leading toenergy efficiency and enhanced user comfort through thedeployment of embedded WSANs A codesign strategy to adistributed control of building lighting systems is describedand an assessment of the cost of WSAN deployment whileachieving particular control performance has been presentedalso In [16] a codesign control algorithm and embeddedplatform for building HVAC systems are described Controlalgorithms are put in place to reduce sensing errors and tooptimize energy cost and monetary cost while satisfying theconstraints for user comfort level

Yahiaouti and Sahraoui in [17] use distributed simulationsto investigate the impact of advanced control systems onbuilding performance applications through virtual represen-tations rather than using experimental trials which are usu-ally time-consuming and cost prohibitive Authors describethe development and implementation of a framework fordistributed simulations involving different software tools overa network In [18] study on parameter-adaptive building(PAB) model which captures system dynamics through anonline estimation of time-varying parameters of a buildingmodel is carried out which helps to reducemodel uncertaintyand can be used for both modeling and control An MPC(model predictive control) framework that is robust againstadditive uncertainty has also been described

In [19] authors suggest a system that adapts its behavioraccording to the past ldquodiscomfortrdquo and thus plays the dualrole of saving energy when discomfort is smaller than thetarget budget and maintaining comfort when the discomfortmargin is small Kastner et al [20] explain the task of buildingautomation and communications infrastructure necessaryto address it An overview of relevant standards is givenincluding the open standards BACnet and LonWorks that arecommonly adopted in the building automation domain Xiaet al [21] examine some of the major QoS challenges raisedby WSANs used for building cyber-physical control sys-tems including resource constraints platform heterogeneitydynamic network topology and mixed traffic The paperfocuses on addressing the problem of network reliability(measuring packet loss-rate PLR) and presenting predictionalgorithm to solve the issue

22 Occupancy Based IBAS Occupancy based control ofbuilding for lighting HVAC and so forth is a relatively newarea A study on how the fine-grained occupancy informationfrom various sensors helps to improve the performance ofoccupant-driven demand control measures in automated

office buildings has been conducted in [22] It also discussesthe pros and cons of the experimental results from theperformance evaluation of chair sensors in an office buildingfor providing fine-grained occupancy information Power-efficient occupancy based energy management (POEM) sys-tem is introduced in [23] for optimally controlling HVACsystems in buildings based on actual occupancy levels It con-sists of wireless network of cameras (OPTNet) that functionsas an optical turnstile to measure areazone occupanciesAnother wireless sensor network of passive infrared (PIR)sensors functions alongside OPTNet Energy efficiency isachieved through combining both the prediction model andcurrent occupancy measured using sensors Authors claim30 energy saving without sacrificing thermal comfort basedon live tests

Occupancy pattern extraction and prediction in an intel-ligent inhabited environment are addressed in [24]The dailybehavioral patterns of the occupant are extracted using awireless sensor network and a recurrent dynamic networkprediction model is built with feedback connections enclos-ing several layers of a Nonlinear Autoregressive Networkwith Exogenous (NARX) inputs network and authors claimedbetter prediction results Sookoor and Whitehouse in [10]presented an occupancy based room level zoning of a cen-tralized HVAC system usingWSAN and a 15 energy savinghas been reported through experimental verification Zhouet al [25] developed a demand-based supervisory control torealize temperature control only for occupied zones whileconsidering the thermal coupling between occupied andunoccupied zones

23 Controller Design for IBAS Dobbs and Hencey in [26]demonstrate the use of model predictive control with astochastic occupancy model to reduce HVAC energy con-sumption They incorporate the buildingrsquos thermal prop-erties local weather predictions and self-tuning stochas-tic occupancy model to reduce energy consumption whilemaintaining occupant comfort A prediction-weighted costfunction provides conditioning of thermal zones before occu-pancy begins and reduces system output before occupancyends and the occupancy model requires no manual trainingand adapts to changes in occupancy patterns during oper-ation In [27] authors describe a multistep ahead predictorfor the MPC control and a two-stage identification processknown as MPC relevant identification technique (MRI)for multistep predictor It also proposes a new two-levelcontrol strategy which enables the formulation of a convexoptimization problem within the MPC control Algorithmhas been applied on a real occupied office building where itreduced energy consumption by 17 in average

The design of decentralized Networked Control Systemshas been considered in [28] It explains the methods tohandle the effects of packet dropouts transmission delaysand so forth with the decentralized NCS design Donkers etal analyse the stability of the NCS based on stochasticallytime-varying discrete-time switched linear system frame-work in [29] They have provided conditions for stability inthe mean square sense using a convex over approximationand a finite number of linear matrix inequalities (LMIs)


Elmahdi [30] introduces a general framework that converts ageneric decentralized control configuration of nonnetworkedsystems to the general setup of NCS An observer basedoutput feedback controller design problem has presented in[31] for Networked Control Systems with packet dropoutsIn this paper dynamical systems approach and the averagedwell-time method have been used Sufficient conditionsfor the exponential stability of the closed loop NCS arederived in terms of nonlinear matrix inequalities and therelation between the packet dropout rate and the stabilityof the closed loop NCS is established An observer basedoutput feedback controller design has been employed usingan iterative algorithm

In all the works reviewed above authors presented dif-ferent methods and techniques for energy saving of BAS invarious aspects However to the best of our knowledge nowork has considered energy saving potential of BAS for bothcontrol subsystem and wireless communication subsystemAlso we are not aware of anywork that deals with the stabilityaspects of NCS due to unreliable network links for dynamicoccupancy based energy management system Thus unlikethe previous works we consider the stability of the NCS inthe presence of packet losses due to unreliable wireless linksintelligent energy management and occupant comfort leveladjustments in the proposed BAS framework

3 Proposed Architecture

The large floor area is assumed to be divided into differentthermal zones based on the VAV box location Figure 1 isthe modified diagram of a building zone (Z0009) generatedusing BRCM toolbox [32] The wireless sensor networkconsists of different sensors for measuring occupancy tem-perature light and air quality The occupancy and its flowrate can be measured accurately using sensors with varyinggranular information and of implicitexplicit type [33 34]To obtain the optimum values for indoor climate basedon the occupancy rate we have formulated and solved amultiobjective optimization problem of energy consumptionand user comfort using NSGA-II [35]

The different zone categories their comfort level andenergy consumption requirements and their priorities forwireless channel access are as follows

Prime zone (P-zone) it is large occupancy levelwith a high rate of change of occupancy it needshigh comfort level and energy consumption and thehighest priority in wireless traffic accessNormal zone (N-zone) occupancy level is in theexpected range and the rate of change of occupancyis not high with moderate comfort level and energyconsumption requirements priority status is highMinimal zone (M-zone) occupancy is lower with asmall rate of change of occupancy it requires themin-imum comfort level and lower energy consumptionwith low priority statusVacant zones (V-zone) it is almost zero or of very lowoccupancy with the least rate of change in occupancy

N-zone

V-zone

P-zone Z0009

ActuatorLocal controllerSensor nodeZone coordinator

OccupantWireless linksGateway

10

9

9

8

8

7

7

6

65

43

21

0173

174175

176177

178179

Z

Y

X

Figure 1 Schematic showing the different priority zones in IBAS

status it requires the least comfort level and energyconsumption with the lowest priority status Thezones belong to any of these categories at a given pointof time

The proposed architecture for wireless networked BASis shown in Figure 2 Sensor outputs for occupancy tem-perature illumination and air quality (119874119896 119879119896 119871119896 and119868119896) are forwarded to the centralized coordinatorcontrollerZonesrsquo status priority and associated weights in the objectivefunctions are determined at central fuzzy inference enginebased on the occupancy level (see Figure 2) The inputs tothe fuzzy inference engine [36 37] are occupancy density andchange of occupancy (difference between the present occu-pancy density and the previous occupancy density) obtainedfrom the processing of occupancy sensor measurementsThegateway block responsible for the prioritization of trafficthrough the network communicates the status of each zone(119878119911) to the corresponding zone coordinator node Herethe EY-NPMA scheme integrated with the Wi-Fi protocol(discussed in Section 32) imparts priority to different zoneclasses during the priority phase and to zones in the sameclass using the burst signal sequences during eliminationand yield phases The difference between the two QoS MACprotocols 80211e protocol [38] and the EY-Wi-Fi [39] isin the inclusion of the elimination phase which helps us toassign priority further among zones with the same accesscategory class at the expense of increased overhead Authorsin [40 41] established that the performance of EY-Wi-Fi isbetter than 80211e in terms of packet delay jitter and packetdelivery ratio

The optimum desired values of climate control for zone-119911 (119879119911 119871119911 119868119911) obtained using multiobjective optimization


Gateway

LMI solver(SDP)

Fuzzy logic rule engine

Optimization algorithm (NSGAII)

Prime zonePrime zoneVacant zone

EY-Wi-Fi

Server

Central coordinatorcontrol

Figure 2 Architecture of CPS for wireless IBAS

algorithm NSGA-II (discussed in Section 33) to meet therequirements of user comfort and energy consumption ofeach zone were communicated to the local distributed con-trollers The optimized transmit power levels (119875119894) of sensornodes matching the zonersquos occupancy status and the rate ofsampling are computed at each sensor node (discussed inSection 34) The distributed local controllers are designedto ensure stability of the closed loop control system overwireless network in the case of unreliable channel conditions(discussed in Section 35)

Controller gains are obtained via solving linear matrixinequalities (LMIs) through semidefinite programming(SDP) [42] Resources available for climate control withina zone are termed as ldquoown resourcesrdquo and those availablein nearby zones are termed as ldquoneighboring resourcesrdquoIn several circumstances based on the demand for quickresponse in comfort control the adjacent vacant or minimalzonesrsquo resources also should be utilized along with the primezonesrsquo resources [25] Control and tracking of neighboring

resources are entrusted with central coordinatorcontrolmodule The sequence of functions of the proposed architec-ture is shown in the steps as follows

(1) activate WSN(2) compute occupancy and change in occupancy using

advanced occupancy sensors(3) categorize the shared space area into P N M and V

zones and set the sample rates using fuzzy inferenceengine Assign priority to sensors among equal statuszones via EY-NPMA and run the optimization algo-rithm (NSGA-II) at centralized controlcoordinator

(4) select the appropriate gains of distributed controllervia SDP to operate the actuator at the optimized setpoint values switch nodes to the appropriate powerlevels using algorithm run at nodes

(5) control and track the indoor environment using ownresources in the zone


Table 1 Fuzzy rules for zone status

Change of occupancyNB NS Z PS PB

OccupancyVL V V V V ML V V M M NAV M M M N NH M N N N PVH N P P P P

Table 2 Fuzzy rules for weights


OccupancyVL L L L AV AVL L L L AV HAV AV AV H H HH AV H H VH VHVH H VH VH VH VH

(6) identify the neighbouring resources that should beoperated to increase the comfort level through cen-tralized controlcoordinator

(7) control and track the neighbouring resources(8) compute occupancy and change in occupancy if it

varies from that of previous sample identify the newstatus of zone and repeat the steps (3)ndash(7)

31 Fuzzy Logic Inference Engine The density of occupancyand change of density are the inputs to the proposed fuzzyrule engineThe outputs of the fuzzy system are the zone pri-orities and their sampling rates and weights to the objectivefunctions of the optimization blockThe output of each rule iscalculated by the rule evaluation method (REM) [37] and theresults aremapped to a consequence classTheweight outputscorresponding to occupancy status from fuzzy block are givento the optimization algorithm for selecting optimum comfortlevel settings for various zones while keeping the energyconsumption rate low Tables 1 and 2 show the fuzzy rules

The linguistic variables used in Tables 1 and 2 are asfollows VH very high H high AV average L low VL verylow NB negative big NS negative small Z zero PS positivesmall PB positive big P N M and V are zone statuses asdefined earlier Occupancy and change of occupancy inputshave trapezoidal and triangular membership functions Theoutputs zone status and weights have singleton and triangu-lar membership functions respectivelyWhen the occupancystatus is VH and change of occupancy is NB then the zonestatus is N and the weight assigned is H Similarly we caninterpret all the rules as shown in the tables

32 EY-Wi-Fi Medium Access Protocol In accordance withthe occupancy status distinct priorities are to be given to thesensors in different zones by using a QoS MAC We chose

Priority phase Yield phaseElimination phase

Data

ACK

Assertion slots

z1

z2

z3

Figure 3 EY-Wi-Fi access mechanism

EY-NPMA [40] enabled Wi-Fi (EY-Wi-Fi) rather than IEEE80211e because of the ability of the former one to furtherdifferentiate the sensors among the same priority class zones

Zones belonging to the same priority class need to befurther prioritized based on the rate of change of occupancyOnly the nodes with equal priorities compete in the elimina-tion phase (second phase)They try tomake the channel busyby transmitting a burst signal of random lengthThose nodesthat do not transmit for the longest duration are eliminatedIn the yield phase (third phase) the nodes that send the burstsignal earliest win the contention and start the data packettransmission The channel access mechanism of EY-NPMAis shown in Figure 3 In this figure we have considered threeP-zones (1199111 1199112 and 1199113) contending for the channel accessWith all three being prime zones they possess equal prioritystatus with the same CWmin (contention windowminimum)and AIFS (arbitrary interframe space) values and enter intothe elimination phase by the transmission of assertion slot Inthe elimination phase 1199111 and 1199113 have the same burst lengthlonger than that of 1199112 so they move into the yield phase Inthe yield phase 1199113 wins the contention and starts data packettransmission as it transmits the shorter yield burst sequencecompared to that of 1199111 Priority can be assigned among N-zones or M-zones in a similar way

33 Nondominated Sorting Genetic Algorithm-II (NSGA-II)The main objectives of the proposed intelligent control ofbuilding space over wireless network are (i) to minimize thetotal energy consumption of the building space comprisingmultiple thermal zones with dynamic occupancy and (ii) tomaximize the comfort level of occupants of the zones throughmaintaining a desirable climate NSGA-II is a multiobjectiveevolutionary algorithm capable of finding multiple Pareto-optimal solutions in a single stretch of simulation itself ThePareto-optimal front presents a number of viable solutionsfor the multiobjective problem which cannot optimize allthe objectives simultaneously NSGA-II has the advantages oflow computational requirements and elitism as compared toNSGA [35] Once the population (solution set) is initializedthe population is sorted based on nondomination into eachfront Each solution is assigned a fitness (or rank) equal toits nondomination level (1 is the best level 2 is the next-bestlevel and so on) Thus minimization of fitness is assumed


Initial population

(size N) Newpopulation(size 2N)

Rank 1

Rank 4

Rank 3

Rank 2

Rank 3

Rank 2

Rank 1

Figure 4 NSGA-II algorithm

with the first front being completely nondominant set in thecurrent population and the second front being dominated bythe individuals in the first front only and thus each frontis formed in this manner NSGA-II algorithm working isdepicted in Figure 4

In addition to fitness value a parameter called crowdingdistance is calculated for each individual The crowdingdistance is a measure of how close an individual is to itsneighbors Large average crowding distance will result inbetter diversity in the population Parents are selected fromthe population by using binary tournament selection basedon the rank and crowding distance An individual is selectedif the rank is lesser than that of the others or if crowding

distance is greater among the individuals in the same front towhich it belongsThe selected population generates offspringsfrom crossover and mutation operators The population withthe current population and current offsprings is sorted againbased on nondomination and only the best 119873 individualsare selected where 119873 is the population size The selection isbased on the rank and the on the crowding distance on thelast front Following [43] the first objective ofminimizing thetotal energy consumption can be expressed as follows

min 119864 =

119899

sum

119911=1

119908119911 (119864119879119911 (119909119879) + 119864119871119911 (119909119871) + 119864119868119911 (119909119868))

st 119864119879119911 le 119864119879max

119864119871119911 le 119864119871max

119864119868119911 le 119864119868max

(1)

where 119864 is the total energy consumption of the buildingspace 119864119879119911 is the energy expenditure to maintain the desiredtemperature in zone 119911 119864119871119911 is to provide lighting in zone 119911and 119864119868119911 is to keep the required air quality level of the zone 119911The decision variables associated with energy expendituresare represented by 119909119879 119909119871 and 119909119868 respectively The weightcommunicated from fuzzy logic rule engine is represented asldquo119908119911rdquo and ldquo119899rdquo represents the total number of thermal zonesin the shared space Following [43] the second objective ofmaximizing the comfort level of occupants (ie minimizingthe occupantsrsquo discomfort level) can be expressed in terms ofoccupant discomfort factor (ODF) as follows

min ODF =

119899

sum

119911=1

1 minus (1 minus 119908119911) ([1 minus (119909119879 minus 119879119911

119879119911

)

2

] + [1 minus (119909119871 minus 119871119911

119871119911

)

2

] + [1 minus (119909119868 minus 119868

119911

119868119911

)

2

])

st 119879min le 119879119911 le 119879max

119871min le 119871119911 le 119871max

119868min le 119868119911 le 119868max

(2)

119879119911 119871119911 and 119868119911 are representing the zonal values of tem-perature illumination and air quality respectively Thismultiobjective optimization problem is solved using NSGA-II as described earlier

34 Power Scheduling inWireless Sensor Nodes TheproposedIBAS framework addresses energy efficiency of not only thecontrol subsystem but also the communication subsystemThe energy consumption of the sensor nodes is reduced by anefficient power scheduling algorithm which can increase thebattery life of sensor nodes and extend the network lifetimealso The amount of energy consumed (119864stx) for sending 119896-bit message over wireless link with a distance of betweentransmitter and receiver is [44]

119864stx = 119864elec119896 + 119864119891119904119896119889

2 119889 lt 1198890

119864elec119896 + 1198641198911198891198961198892 119889 ge 1198890

(3)

where 119864elec is the fixed energy consumed in the transmitterand 119864119891119904 is the energy consumption per unit distance inchannel propagation and

1198890 = radic119864119891119904

119864119891119889

(4)

Different power levels are associated with the differentoperation modes of a sensor node The power states of thenodes can be linked with the status of its zone based on theoccupancy Table 3 summarizes the details of sensor nodestates [45] Power saving in wireless networked sensor nodesis achieved using a power scheduling algorithm proposed in[46] All nodes in a P-zone are assumed to be in 1198780 statewhich is the highest power level state Some of the nodes canbe either in 1198781 or 1198782 states when the zone is with normal orminimal occupancy Most of the nodes in vacant zone are


Table 3 Power states of sensor nodes

State Processor Memory Sensor Radio1198780 Active Active on 119879119909 1198771199091198781 Ideal Sleep on 119877119909

1198782 Sleep Sleep on 119877119909

1198783

Sleep Sleep on off

in 1198783 state which is the lowest power level state Dependingon the dynamic occupancy pattern the nodes can selectappropriate states for minimizing the energy consumption insensor network This concept of switching between differentpower level states is shown in Figure 5 The sensor nodewhich is operating in state 1198780 with power consumption 1198751198780

at time 1199051 changes the state to 1198781 with power consumption1198751198781 where 1198751198780 gt 1198751198781The switching time between state 1198780 and1198781 is 11990511987801198781 and the energy consumed is 11990511987801198781(1198751198780 +1198751198781)2 Thesensor node remains in that state for time 1199051198780minus11990511987801198781 (1199051198780 timeduration for which node remains in 1198780 if there is no switchingto low power level) The energy consumption in state 1198780 for1199051198780 is 11987511987801199051198780The total energy saving is given by the area underthe ldquoABCDArdquo in Figure 5 as follows

119864119878saved =(1199051198780 minus 11990511987801198781)

2(1198751198780 minus 1198751198781) (5)

The energy expenditure needed to bring back the sensor nodefrom 1198751198781 to 1198751198780 at 1199052 is

119864119878expend =11990511987811198780 (1198751198780 + 1198751198781)

2 (6)

Transition from the higher power level to lower power level isbeneficial only if the time interval 1199051198780 is large so that 119864119878(saved)is greater than 119864119878(expend)

1199051198780 gt1

2(11990511987801198781 +

1198751198780 + 1198751198781

1198751198780 minus 1198751198781

11990511987811198780) (7)

This is applicable to the transitions between other powerstates of the sensor node State transition scheduling isdone taking several factors into consideration like energysaving and user comfort in addition to the communicationand processing abilities Transition times for discrete statetransitions are shown in Figure 6 based on the data givenin [47] Modeling of the energy consumption of differentnode components in different operation modes and statetransitions are also described in [47] In the power schedulingalgorithm shown in Algorithm 1 ldquo119874rdquo is occupancy ldquo119862rdquo is themaximum capacity of occupancy for each zone ldquo120575119874rdquo is therate of change of occupancy density ldquo119875119878119894rdquo is the sensor nodepower consumption in state 119878119894 and 119905119878119894119878119895 is the transition timefor state change from state 119878119894 to 119878119895 If the occupancy densityis very high (eg greater than 75 of the maximum capacity119862) and the change of occupancy with respect to time is alsoincreasing the thermal zone is assumed to be the status ofprime zone with high user comfort level and high energyconsumption requirements So the sensor node will be in

A

D

B C

t1 t2

tS0

tS0S1tS1S0

PS0

PS1

PS2

PS3

Figure 5 Graph showing the transmit power switching in sensornodes

PS0

PS1

PS2

PS3

11

182120583s128

384120583s

161284120583s

94120583s

12120583s

94120583s

12120583s

ms

ms

ms

Figure 6 State transition times of sensors for switching powerlevels

state 1198780 with power level 1198751198780 and with a sampling rate of 3minutes If the occupancy rate change is decreasing at leastfor a minimum time period 119905119878th in which 119864119878(saved) minus 119864119878(expend)is positive or if the density of occupancy retains greater than50 for the specified time period given in the algorithm thenthe power level is switched to 1198751198781 and the sampling rate is setas 5 minutes If the occupancy density is greater than 50 ofthe specified maximum with a decreasing rate of change orif the occupancy density is higher than 25 the power levelis changed to 1198751198782 and a sampling rate is set as 10 minutes Ifthe zone is almost empty (lt10 of 119862) or more than 25 witha decreasing rate of change for specified 119905119878th value then thepower level is changed to 1198751198783 and the sampling rate is set as15 minutes

35 Distributed Controller Design The local distributed con-trollers in the two-tier control structure (see Figures 1 and2) are linear switched controllers The set point values aredecided by the occupancy driven optimization algorithmsrun at central control block (first-tier) The central controlleralso decides sampling rates associated with priority status ofthe zone A look up table comprising the set of gains forswitched controllers considering the network topology of thezones and all the possible wireless link reliability statuses ismaintained at the local controllers

The set of gains which guarantees closed loop stabil-ity in the mean square sense is synthesized offline usingsemidefinite programming (SDP) in linear matrix inequality(LMI) solvers (see Figure 2) such as YALMIP at the centralcontrol module [42] Different sets of local control laws are


(1) if 120575119874 is positive then(2) switch 119874 do(3) case 119874 gt 75(4) 119875119878119894 is 1198751198780 zone status P sample rate 3min(5) case 119874 gt 50(6) if 119905119878119894 gt 119905119878th then(7) 119875119878119894 is 1198751198781 zone status N sample rate 5min(8) end if(9) case 119874 gt 25(10) if 119905119878119894 gt 119905119878th then(11) 119875119878119894 is 1198751198782 zone status M sample rate 10min(12) end if(13) case 119874 gt 10(14) if 119905119878119894 gt 119905119878th then(15) 119875

119878119894is 1198751198783 Zone status V sample rate 15min

(16) end if(17) else 120575119874 is negative(18) switch O do(19) case 119874 gt 100(20) if 119905119878119894 gt 119905119878th then(21) 119875119878119894 is 1198751198780 zone status P sample rate 3min(22) end if(23) case 119874 gt 75(24) if 119905119878119894 gt 119905119878th then(25) 119875119878119894 is 1198751198781 zone status N sample rate 5min(26) end if(27) case 119874 gt 50(28) if 119905

119878119894gt 119905119878th then

(29) 119875119878119894 is 1198751198782 zone status M sample rate 10min(30) end if(31) case 119874 gt 25(32) if 119905119878119894 gt 119905119878th then(33) 119875119878119894 is 1198751198783 one status V sample rate 15min(34) end if(35) end if

Algorithm 1

derived for every possible network topology (that may arisedue to the wireless link reliability status) eliminating theneed of communication among distributed controllers toget the information of whole network thus reducing theconservativeness of the control lawModel of packet dropoutsbased on a finite-state Markov chain is used in order toexploit the available knowledge about the stochastic natureof the network and improve the closed loop performanceReliability of network links can be represented by meansof an adjacency matrix (connectivity between sensors andactuators) Λ = [120582119894119895]119898times119899 with 120582119894119895 isin (1 0 minus1) Here 120582119894119895 =ldquo1rdquo indicates idealreliable link between actuator-sensor pair(119894 119895) 120582119894119895 = ldquo0rdquo indicates no link and 120582119894119895 = ldquominus1rdquo indicates alossyunreliable link where packet dropout occurs Considerthe linearized model of nonlinear building thermal systemwhich is assumed to be controllable and observable [48]Linear time-invariant discrete-time system is given in (9)Consider

119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879

isin R119899 is the state vector correspond-ing to the sensor outputs of measured temperature light andindoor air quality 119906 = [1199061 119906119899]

119879isin R119899 is the input vector

for actuators 119896 isin 119873 is the time index and 119860 and 119861 aresystem matrices Assume that states and inputs are subject tothe constraints with the maximum values The goal is to finda state feedback gain matrix 119870 isin R119898times119899 such that system (8)in closed loop with control input (9) becomes asymptoticallystable We have

119906 (119896) = 119870119909 (119896) (9)

where119870 isin R119898times119899Thedistributed control law allows actuatorsto exploit the local sensor measurements only as per thenetwork topologyThe structure of119870depends on the networklinks as follows

120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)

where 119896119894119895 is the (119894 119895)th element of 119870The lossy links are characterized by two-state Markov

chains resulting in dynamic network topologyThis aspect is


accounted using statistical means Let 119871 be the total numberof unreliable links in the network All the possible networktopologies at a given time step 119896 can be represented byreplacing every ldquominus1rdquo in the adjacent matrix Λ with eitherldquo1rdquo or ldquo0rdquo thereby obtaining 119897 = 2

119871 matrices Λ 119891 =

[120582119894119895]119898times119899 119891 = 1 119897 The probability distribution of thenetwork configurations has been computed using the two-state Markov chain (MC) for each link [42 49] Let the twostates of the MC be represented as 1198851 and 1198852 The transitionprobability matrix of the Markov chain is represented asfollows

119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)

where 119905119894119895 = Pr[119911(119896 + 1) = 119885119895 | 119911(119896) = 119885119894] An emissionmatrix 119864 = [119890119894119895]2times2119871 with 119890119894119895 = Pr[Λ(119896) = Λ 119895 | 119911(119896) = 119885119894]

is computed The packet dropouts on the network links areassumed to be iid (independent and identically distributed)random variables with drop probability 1198891 while in state 1198851

of the Markov chain and with drop probability 1198892 while instate 1198852 All the unreliable links are mapped as ideal links orno links in Λ 119891 119891 = 1 119897 Clearly we have to design twosets of control gains 11987011 1198701119897 and 11987021 1198702119897 andthe switching control can be defined using these gains so thatthe closed loop system is asymptotically stable in the meansquare Now we can write switching control law as shown inthe following equation

119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)

Mean square stability condition is given as follows

119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)

where 119876119909 isin R119899times119899 and 119876119906 isin R119898times119898 are weight matrices 119881(119909)

is a switching stochastic Lyapunov function for the closedloop NCS and it is defined as

119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1

Input variable occupancy

L HAV VHVL

Figure 7 Membership functions for fuzzy input variables

The expectations in (13) can be written as

E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)

By substituting 119875119895 = 120574119876119895minus1 119870119895119891 = 119884119895119891119876119895

minus1forall119895 119891 we

can translate (13) to an appropriate LMI condition and bysolving it through SDP problem [42] the required gains 119870119895119891

where 119895 = 1 2 119891 = 1 119897 are obtained The controllerperformance is evaluated in terms of the accumulated stagecost over 119896 = 1 to 119896 = 119896max and is given by

119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)

4 Simulation Results and Discussion

Performance evaluation using simulation for fuzzy rule baseEY-Wi-Fi NSGA-II and controllers are discussed in thissection Fuzzy logic rules were framed to find zone status andweights based on the current occupancy status Simulationwas done using FIS editor of MATLAB Figures 7-8 show theoccupancy and change of occupancy as the input variableswith trapezoidal and triangular membership functions andweight andpriority as the output variableswith triangular andsingleton output membership functions depicted in Figures9-10 respectively

NSGA-II algorithm simulation was done in MATLABwith the parameters given in Table 4 The curve fittinghas been done for obtaining the energy function basedon the data given in [50] The zonersquos various sensor refer-ence values are taken as 70 (K) 750 (lux) and 800 (ppm)respectively Figures 11ndash13 show simulation results for P Nand V zones with energy consumption versus ODF Pareto-optimal fronts In P-zone discomfort values are smaller (highuser comfort value) and power consumption is higher thanthat of other zones The power consumption is reducedin normalminimalvacant zones at the cost of increasein occupant discomfort factor From the obtained Pareto-optimal front values we can choose the desired parameter set


0 04 08 10

05

1

Input variable change in occupancy

NB NS Z PS PB

minus02minus06minus1


0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP

Output variable ldquosample_raterdquo

Figure 9 Membership functions for output variables

Table 4 Parameters of NSGA simulation

Parameters ValuesPopulation size 100Generations 100Pool size 50Crossover distribution index 20Mutation distribution index 20

values corresponding to the occupancy status of the zonesThe whole buildingrsquos energy consumption and user comfortcan be obtained through the summation of individual zonesrsquoenergy consumption and user comfort functions Energysaving of the proposed architecture is found varying basedon the variation in occupancy levels

For illustrating the claim zones shown in Figure 1 arecategorized into prime zone (maximum power consumption119875max = 48KW) normal activity zone (119875max = 37KW) andvacant zone (119875max = 13KW) obtained from the Pareto-fronts depicted in the figures while selecting the valuescorresponding to the maximum occupant comfort levelObtain 31 of energy savings compared with the case inwhich all the zones were treated as prime zones

Implementation of EY-Wi-fi [41] in ns-3 simulator [51]was used for performance evaluation of channel accessprotocol The protocol parameters were chosen followingthe study in [52] The channel access for the case of fournodes is shown in Figure 14 The plots show the durationof transmission for each node (ldquoONrdquo represents channellisteningreceiving and ldquoOFFrdquo represents transmission) withtime Node 2 belonging to a prime zone in Figure 14 has thelongest elimination burst and survives to the yield period

02 04 06 08 10

05

1

Output variable weights

L AV H VH

Figure 10 Membership functions for fuzzy output variables

5101520253035404550

Pow

er (k

W)

03 031 032 033 034 035 036029Occupant discomfort factor

Figure 11 Pareto-front for P-zone

Node 2 wins the contention in yield phase also and begins itsdata packet transmission At the end of the transmission ofnode 2 node 1 which belongs to another prime zone triesto gain access to the channel again It sends a burst signalof longer sequence now and thus it wins the contention andstarts data packet transmission In this fashion all the nodestransmit their data Comparison of the performance of IEEE80211e and EY-Wi-Fi is shown in Figures 15-16 respectivelyProbability of a node to win the contention using 80211e is01726 and the probability of collision is obtained as 01465But the probability of a node to win the contention using EY-Wi-Fi is 04630with a probability of collision equaling 00841Hence the performance of EY-Wi-Fi is found better

The distributed and decentralized controllers were testedusing randomly generated matrices for1198608times8 and 1198618times3 (whichcould not be included due to space limitation) The perfor-mance of the proposed controllers was evaluated throughsimulation using WIDE toolbox [53] in MATLAB platformNetwork topology with three unreliable links and networktopology with six unreliable links were considered Theperformance indices taken are the minimum cost 119869 in (16) toreach the stable equilibrium state of the system and the CPUtime (in seconds) expended for that

Adjacency matrix Λ 1 is

[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)


06 062 064 066 068 07 072 074058Occupant discomfort factor

510152025303540

Pow

er (k

W)

Figure 12 Pareto-front for N-zone

0

2

4

6

8

10

12

14

Pow

er (k

W)

0807507 085 0906 065 095 1055Occupant discomfort factor

Figure 13 Pareto-front for V-zone

On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)

Figure 14 Transmission activity of sensor nodes

500 1000 5000 10000100Number of trials per simulation

012014016018

02022024

Prob

abili

ty o

f win

Figure 15 Probability of win for a node with 80211e

100 500Number of trials per simulation

1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win

Figure 16 Probability of win for a node with EY-Wi-Fi

0 05 1 15 2minus05minus1minus15minus2

minus15

minus1

minus05

0

05

1

15

Figure 17 System poles for topology 1


[[

[

1 minus1 1 0 minus1 0 0 0

0 0 minus1 0 1 minus1 0 0

0 0 minus1 0 0 0 minus1 1

]]

]

(18)

The results of 30 simulation runs are tabulated in Table 5The distributed stochastic controllers have got a higherperformance cost value as the network links become moreand more unreliable That is more control effort is neededto bring back the system to the stable equilibrium state whenthe unreliability is increased Figures 17-18 show the poles ofthe system obtained by the synthesis of distributed stochasticcontrollers with two topologies Initially the systemwasmadeunstable with one pole lying outside the unit circle Openloop poles are marked using ldquotimesrdquo and closed loop poles aremarked using ldquo0rdquoTheCPU time required to solve SDP to finddecentralized controller gains which guarantee stability alsoshoots up if there are more number of unreliable links Wehave run the simulation on Intel i5 25 GHz processor with4GB RAM

Even though the performance of the proposed techniquescould not be evaluated on experimental basis as that of nowwe believe firmly that the proposed methods can achieveenergy savings in the wirelessly networked building zoneswith varying dynamic occupancy patterns



minus15

minus1

minus05

0

05

1

15


Table 5 Controller performance for different topologies

Topology 1 cost 119869 1859CPU time (sec) 1024


5 Conclusion

In this paper a new architecture of CPS for occupancybased wireless networked Intelligent Building AutomationSystem has been proposed with the objectives to maxi-mize the occupant comfort and minimize the total energyconsumption The proposed architecture is suitable for thedynamically varying occupancy patterns in the shared spacesof commercial buildings Fuzzy logic system and NSGA-II are used to identify the prime zones (where higheroccupancy with large variation occurs) and to optimize theenergy requirement of zones EY-NPMA scheme with 80211wireless LAN enables us to prioritize prime zonesrsquo traffic andhence minimize the channel access delay The distributedlocal controller design ensures stability of system even inthe presence of unreliable network links More efforts areneeded to incorporate estimation algorithms for occupancybased demand control of intelligent building automationIn future we plan to include the design and analysis ofmodel predictive controllers and investigating a suitablemathematical thermal model of building zones also

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] WWolf ldquoCyber-physical systemsrdquo Computer vol 42 no 3 pp88ndash89 2009

[2] C-Y Lin S Zeadally T-S Chen and C-Y Chang ldquoEnablingcyber physical systems with wireless sensor networking tech-nologiesrdquo International Journal of Distributed Sensor Networksvol 2012 Article ID 489794 21 pages 2012

[3] A Fisher C Jacobson E A Lee R Murray A Sangiovanni-Vincentelli and E Scholte ldquoIndustrial cyber-physical systemsmdashiCyPhy overview of the research consortiumrdquo Tech Rep 2014

[4] Z-Y Bai and X-Y Huang ldquoDesign and implementation ofa cyber physical system for building smart living spacesrdquoInternational Journal of Distributed Sensor Networks vol 2012Article ID 764186 9 pages 2012

[5] R A Gupta and M-Y Chow ldquoNetworked control systemoverview and research trendsrdquo IEEE Transactions on IndustrialElectronics vol 57 no 7 pp 2527ndash2535 2010

[6] USGBC 2014 httpwwwgreenbuildingcongresscomsitemmbaseattachments4263631Indranil IGBC Networked lightingcontrols for commercial buildings PHILIPSpdf

[7] J P Hespanha P Naghshtabrizi and Y Xu ldquoA survey of recentresults in networked control systemsrdquo Proceedings of the IEEEvol 95 no 1 pp 138ndash162 2007

[8] Z Wang and L Wang ldquoOccupancy pattern based intelligentcontrol for improving energy efficiency in buildingsrdquo in Pro-ceedings of the IEEE International Conference on AutomationScience and Engineering (CASE rsquo12) pp 804ndash809 IEEE SeoulRepublic of Korea August 2012

[9] G D Weig ldquoFacilitiesnetcomrdquo 2013 httpwwwfacilitiesnetcombuildingautomationarticlePros-and-Cons-of-Wireless-Building-Automation-Systems-Facilities-Management-Building-Automation-Featurendash13856

[10] T Sookoor and K Whitehouse ldquoRoomZoner occupancy-based room-level zoning of a centralized HVAC systemrdquo inProceedings of the 4th ACMIEEE International Conference onCyber-Physical Systems (ICCPS rsquo13) pp 209ndash218 April 2013

[11] S Goyal H A Ingley and P Barooah ldquoZone-level controlalgorithms based on occupancy information for energy efficientbuildingsrdquo in Proceedings of the American Control Conference(ACC rsquo12) pp 3063ndash3068 Montreal Canada June 2012

[12] S Wang G Zhang B Shen and X Xie ldquoAn integrated schemefor cyber-physical building energymanagement systemrdquo Proce-dia Engineering vol 15 pp 3616ndash3620 2011

[13] S Dawson-Haggerty X Jiang G Tolle J Ortiz and D CullerldquosMAP a simple measurement and actuation profile for physi-cal informationrdquo in Proceedings of the 8th ACM Conference onEmbedded Networked Sensor Systems (SenSys rsquo10) pp 197ndash210ACM Zurich Switzerland November 2010

[14] X Cao J Chen Y Xiao and Y Sun ldquoBuilding-environmentcontrol with wireless sensor and actuator networks centralizedversus distributedrdquo IEEE Transactions on Industrial Electronicsvol 57 no 11 pp 3596ndash3605 2010

[15] A E-DMady G Provan and NWei ldquoDesigning cost-efficientwireless sensoractuator networks for building control systemsrdquoin Proceedings of the 4th ACMWorkshop on Embedded Systemsfor Energy Efficiency in Buildings (BuildSys rsquo12) pp 138ndash144Toronto Canada November 2012

[16] M Maasoumy Q Zhu C Li F Meggers and A VincentellildquoCo-design of control algorithm and embedded platform forbuilding HVAC systemsrdquo in Proceedings of the ACMIEEEInternational Conference on Cyber-Physical Systems (ICCPS rsquo13)pp 61ndash70 IEEE Philadelphia Pa USA April 2013

[17] A Yahiaouti and A-E-K Sahraoui ldquoA framework for dis-tributed control and building performance simulationrdquo inProceedings of the IEEE 21st InternationalWorkshop on EnablingTechnologies Infrastructure for Collaborative Enterprises (WET-ICE rsquo12) pp 232ndash237 Toulouse France June 2012

[18] M Maasoumy M Razmara M Shahbakhti and A S Vincen-telli ldquoHandling model uncertainty in model predictive control


for energy efficient buildingsrdquo Energy amp Buildings vol 77 pp377ndash392 2014

[19] A Majumdar J L Setter J R Dobbs B M Hencey and D HAlbonesi ldquoEnergy-comfort optimization using discomfort his-tory and probabilistic occupancy predictionrdquo in Proceedings ofthe International Green Computing Conference (IGCC rsquo14) pp1ndash10 IEEE Dallas Tex USA November 2014

[20] W Kastner G Neugschwandtner S Soucek and H M New-man ldquoCommunication systems for building automation andcontrolrdquo Proceedings of the IEEE vol 93 no 6 pp 1178ndash12032005

[21] F Xia X Kong andZ Xu ldquoCyber-physical control overwirelesssensor and actuator networks with packet lossrdquo in WirelessNetworking Based Control pp 85ndash102 Springer New York NYUSA 2011

[22] B Balaji J Xu A Nwokafor R Gupta and Y AgarwalldquoSentinel occupancy based HVAC actuation using existingwifi infrastructure within commercial buildingsrdquo in Proceedingsof the 11th ACM Conference on Embedded Networked SensorSystems (SenSys rsquo13) ACM Rome Italy November 2013

[23] V L Erickson S Achleitner and A E Cerpa ldquoPOEM power-efficient occupancy-based energy management systemrdquo in Pro-ceedings of the 12th International Conference on InformationProcessing in Sensor Networks pp 203ndash216 Philadelphia PaUSA April 2013

[24] S M Mahmoud A Lotfi and C Langensiepen ldquoOccupancypattern extraction and prediction in an inhabited intelligentenvironment using NARX networksrdquo in Proceedings of the IEEE6th International Conference on Intelligent Environments (IE rsquo10)pp 58ndash63 July 2010

[25] P Zhou G Huang and Z Li ldquoDemand-based temperaturecontrol of large-scale rooms aided by wireless sensor networkenergy saving potential analysisrdquo Energy and Buildings vol 68pp 532ndash540 2014

[26] J R Dobbs and BM Hencey ldquoModel predictive HVAC controlwith online occupancy modelrdquo Energy amp Buildings vol 82 pp675ndash684 2014

[27] Z Vana J Cigler J Siroky E Zacekova and L Ferkl ldquoModel-based energy efficient control applied to an office buildingrdquoJournal of Process Control vol 24 no 6 pp 790ndash797 2014

[28] L Bakule and M Papık ldquoDecentralized control and communi-cationrdquo Annual Reviews in Control vol 36 no 1 pp 1ndash10 2012

[29] M C F Donkers W P M H Heemels D Bernardini ABemporad and V Shneer ldquoStability analysis of stochasticnetworked control systemsrdquo Automatica vol 48 no 5 pp 917ndash925 2012

[30] A Elmahdi ldquoDecentralized control framework and stabilityanalysis for networked control systemsrdquo ASME Journal ofDynamic Systems Measurement and Control vol 137 no 5Article ID 051006 15 pages 2014

[31] W Zhang and L Yu ldquoOutput feedback stabilization of net-worked control systems with packet dropoutsrdquo IEEE Transac-tions on Automatic Control vol 52 no 9 pp 1705ndash1710 2007

[32] D Sturzenegger D Gyalistras V Semeraro M Morari and RS Smith ldquoBRCM matlab tool box model generation for modelpredictive building controlrdquo in Proceedings of the AmericanControl Conference (ACC rsquo14) Portland Ore USA June 2014

[33] A Marchiori ldquoEnabling distributed building control with wire-less sensor networksrdquo in Proceedings of the IEEE InternationalSymposium on a World of Wireless Mobile and MultimediaNetworks (WoWMoM rsquo11) pp 1ndash3 IEEE Lucca Italy June 2011

[34] T Labeodan W Zeiler G Boxem and Y Zhao ldquoOccupancymeasurement in commercial office buildings for demand-driven control applicationsndasha survey and detection systemevaluationrdquo Energy and Buildings vol 93 pp 303ndash314 2015

[35] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002

[36] M Marin-Perianu and P Havinga ldquoD-FLERmdasha distributedfuzzy logic engine for rule-based wireless sensor networksrdquo inProceedings of the 4th International Symposium on UbiquitousComputing Systems (UCS rsquo07) Tokyo Japan November 2007vol 4836 of Lecture Notes in Computer Science pp 86ndash101Springer Berlin Germany 2007

[37] RAlcala J Alcala-FdezM J Gacto and FHerrera ldquoImprovingfuzzy logic controllers obtained by experts a case study inHVAC systemsrdquo Applied Intelligence vol 31 no 1 pp 15ndash302009

[38] IEEE ldquo80211e-2005mdashIEEE Standard for Information Tech-nologymdashLocal and Metropolitan Area NetworksmdashSpecificRequirementsmdashPart 11 Wireless LANMedium Access Control(MAC) and Physical Layer (PHY) SpecificationsmdashAmendment8 Medium Access Control (MAC) Quality of Service Enhance-mentsrdquo pp 1ndash212 November 2005

[39] P Jacquet P Minet P Muhlethaler and N Rivierre ldquoPriorityand collision detection with active signalingmdashthe channelaccess mechanism of HIPERLANrdquo Wireless Personal Commu-nications vol 4 no 1 pp 11ndash25 1997

[40] P Muhlethaler Y Toor and A Laouiti ldquoSuitability of HIPER-LANrsquos EY-NPMA for traffic jam scenarios in VANETsrdquo inProceedings of the 10th International Conference on IntelligentTransportation Systems Telecommunications (ITST rsquo10) 2010

[41] H Baccouch C Adjih and P Muhlethaler ldquoEy-Wifi activesignaling for the ns-3 80211 modelrdquo Tech Rep 2013

[42] D Barcelli D Bernardini and A Bemporad ldquoSynthesis ofnetworked switching linear decentralized controllersrdquo in Pro-ceedings of the 49th IEEE Conference on Decision and Control(CDC rsquo10) pp 2480ndash2485 December 2010

[43] R Yang and L Wang ldquoMulti-objective optimization fordecision-making of energy and comfort management in build-ing automation and controlrdquo Sustainable Cities and Society vol2 no 1 pp 1ndash7 2012

[44] W R Heinzelman A P Chandrakasan and H Balakrish-nan ldquoEnergy-efficient communication protocol for wirelessmicrosensor networksrdquo in Proceedings of the 33rd AnnualHawaii International Conference on System Siences (HICSS rsquo00)Maui Hawaii USA January 2000

[45] HD ChinhAnalysis design and optimization of energy efficientprotocols for wirless sensor networks [PhD thesis] NationalUniversity Singapore 2013

[46] E Shih S-H Cho N Ickes et al ldquoPhysical layer driven pro-tocol and algorithm design for energy-efficient wireless sensornetworksrdquo in Proceedings of the 7th Annual International Con-ference on Mobile Computing and Networking pp 272ndash286Rome Italy July 2001

[47] H-Y Zhou D-Y Luo Y Gao and D-C Zuo ldquoModeling ofnode energy consumption for wireless sensor networksrdquo Scien-tific Research vol 3 no 1 pp 18ndash23 2014

[48] M Maasoumy and A L Sangiovanni-Vincentelli ldquoModelingand optimal control algorithm design for HVAC systems inenergy efficient buildingsrdquo Tech Rep University of CaliforniaBerkeley Calif USA 2011


[49] X Yu J W Modestino and X Tian ldquoThe accuracy of Gilbertmodels in predicting packet-loss statistics for a single-multi-plexer network modelrdquo in Proceedings of the 24th Annual JointConference of the IEEE Computer and Communications Societies(INFOCOM rsquo05) vol 4 pp 2602ndash2612 March 2005

[50] L Wang Z Wang and R Yang ldquoIntelligent multiagent controlsystem for energy and comfort management in smart andsustainable buildingsrdquo IEEE Transactions on Smart Grid vol 3no 2 pp 605ndash617 2012

[51] Ns-3 June 2013 httpwwwnsnamorg[52] G Dimitriadis and F-N Pavlidou ldquoTwo alternative schemes to

EY-NPMA for medium access in high bitrate wireless LANsrdquoWireless Personal Communications vol 28 no 2 pp 121ndash1422003

[53] WIDE Toolbox httpcselabimtluccaithybridwide

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


compromising the indoor comfort Here the problem isformulated as a critical control system so that the economyand longevity are assured by exploiting the advantages ofmodern communication and control technologies

In order to build intelligence in BAS a sensor networkconsisting of hundreds of sensors in a building can accuratelybe deployed to monitormeasure the temperature air qual-ity light humidity door or windowrsquos openclose positionand occupancy accurately [8] Occupancy sensors can beinstalled to automatically switch the HVAC and lighting sys-tem in accordance with the occupancy status of the buildingzones Actuator nodes in turn would have the responsibilityto control the subsystems within the building zones Energysavings can be more when the separate subsystems cooperateand communicate with each other Integration of thesesubsystems would add more sophistication to the controlsystem and it would be possible to render an intelligentsystem of Building Automation System (BAS) Enhancementof battery life of sensor nodes will naturally lead to networkavailability and system reliability

Looking at the cost factor and deployability it is seenthat the necessity of wireless BAS arises in various situations(i) when wiring is expensive and time-consuming (ii) whenit demands scalability and flexibility in the deployment ofsensoractuator nodes and (iii) when there is need forredeployment or retrofit without affecting the aestheticsof existing buildings [9] With due design considerationsand planning and by adopting appropriate implementationtechniques wireless technology can be used economicallyand efficiently The advantages of wireless technology cannotbe outweighed by the challenges like poor channel condi-tions and competition for channel access which may createunreliable and delayed communication of control and datatraffic Hence intense research efforts are needed to addressthe diverse issues in real time control of BAS over wirelessnetworks using open standards rather than proprietarystandards

The scenario of control that has been considered in thiswork is the automation of large shared spaces of commercialbuildings where big crowd occupies the space and movesfrom one space to another Occupancy pattern changesdynamically and unpredictably thus making the controlneeded for comfort and economy difficult otherwise [10]Normally the settings of the building climate control systemare to be in such a way that occupant comfort level is themaximum However this results into wastage of energy forlighting lamps coolingheating space and for air qualityassurance for unoccupied spaces also Moreover energyis wasted for overcooling and for cooling less occupiedspaces In modern approaches the building thermal zonesare divided based on the positioning of variable air volume(VAV) boxes of HVAC [11] The problem considered here isof a large shared space comprising more than one thermalzone of the building Occupancy patterns vary dynamicallyand the zones are classified into different priority classesThe requirement is that comfort level of heavily occupiedldquoprime zonesrdquo shall be maintained maximum compared tothe lightly occupied zones in concurrence with the energysaving in ldquovacantrdquolightly occupied zones In the proposed

method priority is assigned for wireless traffic of prime zonesusing quality of service (QoS) medium access control (MAC)protocol Emphasis is given to the competition among primezonesrsquos sensors belonging to the same shared space Stabilityof the closed loop control over wireless networks has beenensured while packet drops due to unreliable links existAdditionally the energy consumed by the nodes have tobe minimized to provide longer battery life and extendednetwork availability

The proposed architecture has a hierarchical structurefor communication and control and has the following fea-turesfunctionality (i) it decides the status of a particularzone based on its density and rate of change of occupancyand assigns proportional weights to the objective functionsusing fuzzy logic rule base (ii) it offers priority to the networktraffic of prime zones by QoS differentiated medium accesscontrol (MAC) via Elimination-Yield Nonpreemptive Multi-ple Access (EY-NPMA) scheme adopted withWi-Fi protocol(iii) it optimizes energy consumption and user comfort inevery zone based on occupancy using Nondominated SortedGenetic Algorithm-II (NSGA-II) (iv) it schedules transmitpower and sampling rates of wireless sensor nodes throughthe algorithm proposed (v) it deals with design of distributedlocal controllers to guarantee the stability of the closedloop control in presence of packet drops (due to unreliablenetwork links)

The remaining part of the paper is organized as followsa brief review of the related work is given in Section 2Architecture for an energy-efficient priority-access baseddecentralized controller for wireless BAS is described inSection 3 Sections 31ndash35 explain the fuzzy rule base forzone status selection the concept of EY-NPMA schemethe multiobjective optimization problem formulation usingNSGA-II the sensor node power scheduling algorithm forWSN and the decentralized controller design in the sequelSimulation results and discussions are described in Section 4Paper is concluded in Section 5

2 Related Work

21 Wireless Sensor Networks in Intelligent Building Automa-tion There has been an overwhelming interest in the recentpast for using the advanced technology to make the build-ing control more intelligent Wang et al [12] present abuilding energy management system with wireless sensornetworks using multiagent distributed control methodologythat concentrates on optimized target of air conditioninglighting and official electrical devices A multitier systemview point is used to incorporate the various levels of sensingprocessing communication and management functionalityThe cyber-physical building energy management system(CBEMS) has been assumed with a high level of intelligenceand automation The occupant comfort quality level is not aconcern here Authors in [13] describe a simple web servicecalled the Simple Measuring and Actuation Profile (sMAP)which allows instruments and other producers of physicalinformation to directly publish their data in cyber space Self-describing physical information which is uniform and withmachine independent access would avoid the innumerable


















N-zone

V-zone

P-zone Z0009



10

9

9

8

8

7

7

6

65

43

21

0173

174175

176177

178179

Z

Y

X






Gateway

LMI solver(SDP)




EY-Wi-Fi

Server

























Data

ACK

Assertion slots

z1

z2

z3






Initial population


Rank 1

Rank 4

Rank 3

Rank 2

Rank 3

Rank 2

Rank 1





min 119864 =

119899

sum

119911=1

119908119911 (119864119879119911 (119909119879) + 119864119871119911 (119909119871) + 119864119868119911 (119909119868))

st 119864119879119911 le 119864119879max

119864119871119911 le 119864119871max

119864119868119911 le 119864119868max

(1)


min ODF =

119899

sum

119911=1


119879119911

)

2

] + [1 minus (119909119871 minus 119871119911

119871119911

)

2

] + [1 minus (119909119868 minus 119868

119911

119868119911

)

2

])

st 119879min le 119879119911 le 119879max

119871min le 119871119911 le 119871max

119868min le 119868119911 le 119868max

(2)



119864stx = 119864elec119896 + 119864119891119904119896119889

2 119889 lt 1198890

119864elec119896 + 1198641198911198891198961198892 119889 ge 1198890

(3)


1198890 = radic119864119891119904

119864119891119889

(4)





1198782 Sleep Sleep on 119877119909

1198783

Sleep Sleep on off



119864119878saved =(1199051198780 minus 11990511987801198781)

2(1198751198780 minus 1198751198781) (5)


119864119878expend =11990511987811198780 (1198751198780 + 1198751198781)

2 (6)


1199051198780 gt1

2(11990511987801198781 +

1198751198780 + 1198751198781

1198751198780 minus 1198751198781

11990511987811198780) (7)


A

D

B C

t1 t2

tS0

tS0S1tS1S0

PS0

PS1

PS2

PS3


PS0

PS1

PS2

PS3

11

182120583s128

384120583s

161284120583s

94120583s

12120583s

94120583s

12120583s

ms

ms

ms









119878119894gt 119905119878th then


Algorithm 1


119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879




119906 (119896) = 119870119909 (119896) (9)


120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)





119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























N-zone

V-zone

P-zone Z0009



10

9

9

8

8

7

7

6

65

43

21

0173

174175

176177

178179

Z

Y

X






Gateway

LMI solver(SDP)




EY-Wi-Fi

Server

























Data

ACK

Assertion slots

z1

z2

z3






Initial population


Rank 1

Rank 4

Rank 3

Rank 2

Rank 3

Rank 2

Rank 1





min 119864 =

119899

sum

119911=1

119908119911 (119864119879119911 (119909119879) + 119864119871119911 (119909119871) + 119864119868119911 (119909119868))

st 119864119879119911 le 119864119879max

119864119871119911 le 119864119871max

119864119868119911 le 119864119868max

(1)


min ODF =

119899

sum

119911=1


119879119911

)

2

] + [1 minus (119909119871 minus 119871119911

119871119911

)

2

] + [1 minus (119909119868 minus 119868

119911

119868119911

)

2

])

st 119879min le 119879119911 le 119879max

119871min le 119871119911 le 119871max

119868min le 119868119911 le 119868max

(2)



119864stx = 119864elec119896 + 119864119891119904119896119889

2 119889 lt 1198890

119864elec119896 + 1198641198911198891198961198892 119889 ge 1198890

(3)


1198890 = radic119864119891119904

119864119891119889

(4)





1198782 Sleep Sleep on 119877119909

1198783

Sleep Sleep on off



119864119878saved =(1199051198780 minus 11990511987801198781)

2(1198751198780 minus 1198751198781) (5)


119864119878expend =11990511987811198780 (1198751198780 + 1198751198781)

2 (6)


1199051198780 gt1

2(11990511987801198781 +

1198751198780 + 1198751198781

1198751198780 minus 1198751198781

11990511987811198780) (7)


A

D

B C

t1 t2

tS0

tS0S1tS1S0

PS0

PS1

PS2

PS3


PS0

PS1

PS2

PS3

11

182120583s128

384120583s

161284120583s

94120583s

12120583s

94120583s

12120583s

ms

ms

ms









119878119894gt 119905119878th then


Algorithm 1


119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879




119906 (119896) = 119870119909 (119896) (9)


120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)





119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Gateway

LMI solver(SDP)




EY-Wi-Fi

Server

























Data

ACK

Assertion slots

z1

z2

z3






Initial population


Rank 1

Rank 4

Rank 3

Rank 2

Rank 3

Rank 2

Rank 1





min 119864 =

119899

sum

119911=1

119908119911 (119864119879119911 (119909119879) + 119864119871119911 (119909119871) + 119864119868119911 (119909119868))

st 119864119879119911 le 119864119879max

119864119871119911 le 119864119871max

119864119868119911 le 119864119868max

(1)


min ODF =

119899

sum

119911=1


119879119911

)

2

] + [1 minus (119909119871 minus 119871119911

119871119911

)

2

] + [1 minus (119909119868 minus 119868

119911

119868119911

)

2

])

st 119879min le 119879119911 le 119879max

119871min le 119871119911 le 119871max

119868min le 119868119911 le 119868max

(2)



119864stx = 119864elec119896 + 119864119891119904119896119889

2 119889 lt 1198890

119864elec119896 + 1198641198911198891198961198892 119889 ge 1198890

(3)


1198890 = radic119864119891119904

119864119891119889

(4)





1198782 Sleep Sleep on 119877119909

1198783

Sleep Sleep on off



119864119878saved =(1199051198780 minus 11990511987801198781)

2(1198751198780 minus 1198751198781) (5)


119864119878expend =11990511987811198780 (1198751198780 + 1198751198781)

2 (6)


1199051198780 gt1

2(11990511987801198781 +

1198751198780 + 1198751198781

1198751198780 minus 1198751198781

11990511987811198780) (7)


A

D

B C

t1 t2

tS0

tS0S1tS1S0

PS0

PS1

PS2

PS3


PS0

PS1

PS2

PS3

11

182120583s128

384120583s

161284120583s

94120583s

12120583s

94120583s

12120583s

ms

ms

ms









119878119894gt 119905119878th then


Algorithm 1


119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879




119906 (119896) = 119870119909 (119896) (9)


120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)





119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























Data

ACK

Assertion slots

z1

z2

z3






Initial population


Rank 1

Rank 4

Rank 3

Rank 2

Rank 3

Rank 2

Rank 1





min 119864 =

119899

sum

119911=1

119908119911 (119864119879119911 (119909119879) + 119864119871119911 (119909119871) + 119864119868119911 (119909119868))

st 119864119879119911 le 119864119879max

119864119871119911 le 119864119871max

119864119868119911 le 119864119868max

(1)


min ODF =

119899

sum

119911=1


119879119911

)

2

] + [1 minus (119909119871 minus 119871119911

119871119911

)

2

] + [1 minus (119909119868 minus 119868

119911

119868119911

)

2

])

st 119879min le 119879119911 le 119879max

119871min le 119871119911 le 119871max

119868min le 119868119911 le 119868max

(2)



119864stx = 119864elec119896 + 119864119891119904119896119889

2 119889 lt 1198890

119864elec119896 + 1198641198911198891198961198892 119889 ge 1198890

(3)


1198890 = radic119864119891119904

119864119891119889

(4)





1198782 Sleep Sleep on 119877119909

1198783

Sleep Sleep on off



119864119878saved =(1199051198780 minus 11990511987801198781)

2(1198751198780 minus 1198751198781) (5)


119864119878expend =11990511987811198780 (1198751198780 + 1198751198781)

2 (6)


1199051198780 gt1

2(11990511987801198781 +

1198751198780 + 1198751198781

1198751198780 minus 1198751198781

11990511987811198780) (7)


A

D

B C

t1 t2

tS0

tS0S1tS1S0

PS0

PS1

PS2

PS3


PS0

PS1

PS2

PS3

11

182120583s128

384120583s

161284120583s

94120583s

12120583s

94120583s

12120583s

ms

ms

ms









119878119894gt 119905119878th then


Algorithm 1


119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879




119906 (119896) = 119870119909 (119896) (9)


120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)





119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Initial population


Rank 1

Rank 4

Rank 3

Rank 2

Rank 3

Rank 2

Rank 1





min 119864 =

119899

sum

119911=1

119908119911 (119864119879119911 (119909119879) + 119864119871119911 (119909119871) + 119864119868119911 (119909119868))

st 119864119879119911 le 119864119879max

119864119871119911 le 119864119871max

119864119868119911 le 119864119868max

(1)


min ODF =

119899

sum

119911=1


119879119911

)

2

] + [1 minus (119909119871 minus 119871119911

119871119911

)

2

] + [1 minus (119909119868 minus 119868

119911

119868119911

)

2

])

st 119879min le 119879119911 le 119879max

119871min le 119871119911 le 119871max

119868min le 119868119911 le 119868max

(2)



119864stx = 119864elec119896 + 119864119891119904119896119889

2 119889 lt 1198890

119864elec119896 + 1198641198911198891198961198892 119889 ge 1198890

(3)


1198890 = radic119864119891119904

119864119891119889

(4)





1198782 Sleep Sleep on 119877119909

1198783

Sleep Sleep on off



119864119878saved =(1199051198780 minus 11990511987801198781)

2(1198751198780 minus 1198751198781) (5)


119864119878expend =11990511987811198780 (1198751198780 + 1198751198781)

2 (6)


1199051198780 gt1

2(11990511987801198781 +

1198751198780 + 1198751198781

1198751198780 minus 1198751198781

11990511987811198780) (7)


A

D

B C

t1 t2

tS0

tS0S1tS1S0

PS0

PS1

PS2

PS3


PS0

PS1

PS2

PS3

11

182120583s128

384120583s

161284120583s

94120583s

12120583s

94120583s

12120583s

ms

ms

ms









119878119894gt 119905119878th then


Algorithm 1


119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879




119906 (119896) = 119870119909 (119896) (9)


120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)





119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1198782 Sleep Sleep on 119877119909

1198783

Sleep Sleep on off



119864119878saved =(1199051198780 minus 11990511987801198781)

2(1198751198780 minus 1198751198781) (5)


119864119878expend =11990511987811198780 (1198751198780 + 1198751198781)

2 (6)


1199051198780 gt1

2(11990511987801198781 +

1198751198780 + 1198751198781

1198751198780 minus 1198751198781

11990511987811198780) (7)


A

D

B C

t1 t2

tS0

tS0S1tS1S0

PS0

PS1

PS2

PS3


PS0

PS1

PS2

PS3

11

182120583s128

384120583s

161284120583s

94120583s

12120583s

94120583s

12120583s

ms

ms

ms









119878119894gt 119905119878th then


Algorithm 1


119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879




119906 (119896) = 119870119909 (119896) (9)


120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)





119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119878119894gt 119905119878th then


Algorithm 1


119909 (119896 + 1) = 119860119909 (119896) + 119861119906 (119896) (8)

where 119909 = [1199091 119909119899]119879




119906 (119896) = 119870119909 (119896) (9)


120582119894119895 = 0 997904rArr 119896119894119895 = 0 (10)





119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119871 matrices Λ 119891 =


119879 = [1199021 1 minus 1199021

1 minus 1199022 1199022

] = [119905119894119895]2times2 (11)




119906 (119896) =

11987011119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 1

1198701119897119909 (119896) if 119911 (119896) = 1198851 Λ (119896) = Λ 119897

11987021119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 1

1198702119897119909 (119896) if 119911 (119896) = 1198852 Λ (119896) = Λ 119897

(12)


119864 [119881 (119909 (119896 + 1))] minus 119881 (119909 (119896))

le minus119909 (119896)119879119876119909119909 (119896) minus 119864 [119906 (119896)

119879119876119906119906 (119896)]

(13)



119906 (119896) =

119909 (119896)1198791198751119909 (119896) if 119911 (119896) = 1198851

119909 (119896)1198791198752119909 (119896) if 119911 (119896) = 1198852

(14)

0 02 04 06 08 10

05

1


L HAV VHVL



E [119881 (119909 (119896 + 1))] =

ℓ

sum

119891=1

2

sum

119911=1

119890119895119891119905119895119911119909 (119896)119879(119860 + 119861119870119895119891)

119879

sdot 119875119911 (119860 + 119861119870119895119891) 119909 (119896)

E [119906 (119896)119879119876119906119906 (119896)] =

ℓ

sum

119891=1

119890119895119891119909 (119896)119879119870119879

119895119891119876119906119870119895119891119909 (119896)

(15)





119869 =

119896max

sum

119896=1

(1003817100381710038171003817119876119909119909 (119896)

10038171003817100381710038172 +1003817100381710038171003817119876119906119906 (119896)

10038171003817100381710038172) (16)





0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 04 08 10

05

1


NB NS Z PS PB



0 2 4 6 8 10 12 14 16 18 200

05

1 VMNP








02 04 06 08 10

05

1


L AV H VH


5101520253035404550

Pow

er (k

W)






[[

[

1 1 1 0 minus1 0 0 0

0 0 minus1 0 1 1 0 0

0 0 minus1 0 0 0 1 1

]]

]

(17)



510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











510152025303540

Pow

er (k

W)


0

2

4

6

8

10

12

14

Pow

er (k

W)



On

Off

Node 0Node 1

Node 2Node 3

6259

6258

626

6257

6261

6262

6256

6264

6265

6263

6255

6266

Time (s)



012014016018

02022024

Prob

abili

ty o

f win



1000 5000 10000

03804

042044046048

05052

Prob

abili

ty o

f win



minus15

minus1

minus05

0

05

1

15



[[

[




]]

]

(18)





minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











minus15

minus1

minus05

0

05

1

15





5 Conclusion




References
































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article An Occupancy Based Cyber-Physical...

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