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IN REVIEW, SPECIAL ISSUE ON NEURODYNAMIC SYSTEMS FOR OPTIMIZATION AND APPLICATIONS. 1

Nonlinear Model Predictive Control of A GasolineHCCI Engine Using Extreme Learning Machines

Vijay Manikandan Janakiraman, XuanLong Nguyen, and Dennis Assanis

Abstract—Homogeneous charge compression ignition (HCCI)is a futuristic combustion technology that operates with a highfuel efficiency and reduced emissions. HCCI combustion is char-acterized by complex nonlinear dynamics which necessitates amodel based control approach for automotive application. HCCIengine control is a nonlinear, multi-input multi-output problemwith state and actuator constraints which makes controller designa challenging task. Typical HCCI controllers make use of a firstprinciples based model which involves a long development timeand cost associated with expert labor and calibration. In thispaper, an alternative approach based on machine learning ispresented using extreme learning machines (ELM) and nonlinearmodel predictive control (MPC). A recurrent ELM is used tolearn the nonlinear dynamics of HCCI engine using experimentaldata and is shown to accurately predict the engine behaviorseveral steps ahead in time, suitable for predictive control. Usingthe ELM engine models, an MPC based control algorithm witha simplified quadratic program update is derived for real timeimplementation. The working and effectiveness of the MPCapproach has been analyzed on a nonlinear HCCI engine modelfor tracking multiple reference quantities along with constraintsdefined by HCCI states, actuators and operational limits.

Index Terms—Recurrent Neural Networks, Extreme LearningMachines, Model Predictive Control, Nonlinear MPC, NonlinearIdentification, Engine Control, Control Model, HomogeneousCharge Compression Ignition, HCCI Engine.

I. INTRODUCTION

In recent years, the requirements on automotive perfor-mance, emissions and cost have become increasingly stringent.As a consequence, the auto industry has been continuouslyintroducing efficient mechanisms to meet these demands [1].Invariably, such systems introduce additional complexity andassociated challenges in design and implementation. Homo-geneous charge compression ignition (HCCI) is an advancedcombustion technology incorporating several of the recentautomotive advancements including variable valve timing,exhaust gas recirculation, intake charge boosting etc [1]. HCCIengines shifted the spotlight from traditional spark ignited (SI)and compression ignited (CI) engines owing to its ability toreduce emissions and fuel consumption significantly [2], [3].However, HCCI poses several challenges for implementation.These include the absence of a direct trigger for combus-tion, narrow operating range and high sensitivity to ambientconditions amongst others. Control of HCCI combustion is a

Vijay Manikandan Janakiraman is with NASA Ames Research Center(UARC), Moffett Field, CA, USA. He was previously with the Departmentof Mechanical Engineering, University of Michigan, Ann Arbor, MI, USAe-mail: [email protected].

XuanLong Nguyen is with the Department of Statistics, University ofMichigan, Ann Arbor, MI, USA.

Dennis Assanis is with the Stony Brook University, NY, USA.

challenging problem and a model based approach is typicallyemployed [4], [5], where a control-oriented reduced ordermodel is developed using first principles. Such models involvea long development time and cost associated with expert laborand calibration. To accelerate HCCI implementation on auto-motive applications, a key requirement is to develop predictivedynamic models quickly that can not only capture the requireddynamics for control but also operate under limited resources,for instance, onboard an engine electronic control unit (ECU)whose memory and computation are limited.

In order to enable the complex control strategies, the HCCIengine is equipped with additional sensors such as in-cylinderpressure transducers that can provide valuable operationaldata. In-cylinder pressure data can give insights into the gen-eral combustion behavior of an engine, including efficiency,emissions and stability. Although the primary use is to observethe states of the engine for feedback control [6], [7], suchsensory information can be processed to develop dynamicmodels of the system itself. It has been previously shown bythe authors that in-cylinder pressure data can be used to de-velop control oriented models of engine combustion phasing,work output, combustion stability using neural networks [8]and support vector machines [9], [10]. This article considerscontroller design for HCCI engine using data based models.Control systems using machine learning models are popularin robotics, autonomous and aerospace systems [11], [12]but less popular in the automotive industry. However, withincrease in complexity of emerging systems and with advancedsensing capabilities, there is a significant need to identifynew venues and evaluate the potential of information basedmodels for automotive control applications. This forms themain motivation of the interdisciplinary research consideredin this article.

For the HCCI modeling problem, Extreme Learning Ma-chines (ELM) were selected for their fast operation andapproximation capabilities to fit nonlinear systems [13]. Also,when ELM is trained with real world experimental data, itapproximates the real system and makes no (or minimal)simplifying assumptions about the underlying phenomena. Thedynamics of sensors, actuators and other complex processeswhich are usually overlooked/hard to model using first prin-ciples, can be captured using the identification method. Inaddition, for a system like the combustion engine, prototypehardware is typically available and extensive experimentaldata can be collected making the data based approach moreappropriate. Data based identification is less common forHCCI engines owing to its nonlinear, highly sensitive andunstable behavior. However, it has been shown previously

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by the authors that artificial neural networks [8] and supportvector machines [9] are indeed suited for accurately predictingthe dynamics of HCCI. However, artificial neural networks(based on backpropagation) have issues with picking up alocal minima while support vector machines result in a largenumber of parameters making it unsuitable for real engineimplementations [9]. ELMs on the other hand, solve a convexproblem resulting in a global optimal solution and simple tobe implemented onboard the engine ECU to make predictions.

For the HCCI control problem, a model predictive control(MPC) framework is employed that can operate with blackbox models [14]. In addition, MPC is well suited for handlingoperation related and hardware related constraints in an elegantmanner. Even for simple linear systems, MPC has been shownto perform well against traditional control such as PID [15],LQ control [16], [17] etc. Typically, MPC makes use of amathematical model of the system and solves an optimizationproblem with the given constraints to achieve an optimalcontrol solution [15]. In this paper, a recurrent ELM enginemodel is used to make predictions which are then used byMPC to make control decisions for tracking a given referencecommand. Model predictive control has been quite popular inthe automotive domain for both spark ignited [18] and com-pression ignited engines [19], [20]. However, the applicationof MPC to HCCI engines is at an early stage involving physicsbased models [21], [22] and simple identification models [23].This article advances the MPC application to HCCI enginesby demonstrating on a data based non-linear model that couldcapture more complex behavior of the engine.

The contributions of the article can be summarized asfollows. An ELM based system identification framework isdeveloped for modeling the HCCI engine from real experimen-tal data. This include optimal model selection (tuning modelhyper-parameters), training and validation of the model to theHCCI engine data. An ELM based MPC framework is not re-ported in the literature to the best of the authors knowledge. Acontrol oriented model of the gasoline HCCI engine predictingengine work output, combustion phasing, combustion stabilityin terms of maximum pressure and maximum pressure rise rateetc. is developed using ELM models and validated at severaloperating conditions. A model predictive control frameworkbased on linearized ELM and a simplified quadratic programupdate is developed for the HCCI system suitable for real-timeapplication. The article finally identifies the HCCI engine asa novel application domain for demonstration of the abovemethodologies in combination.

The article is organized as follows. The HCCI engineexperimental setup, design of experiments and data collectionare summarized in section II. A system identification proce-dure using ELM is described in section III where predictivemodels are developed and validated using HCCI experimentaldata. A model predictive control algorithm using linearizedELM models is derived in section IV where linearization isdone using the structure of ELM to avoid numerical gradi-ent calculations. Finally, the ELM based MPC approach isdemonstrated in simulations in section V. A fast quadraticprogramming method is employed using the convex nature ofthe problem which enables real-time implementation of the

controller. Simulation cases have been analyzed to understandthe working and effectiveness of the proposed method.

II. HCCI ENGINE SYSTEM AND EXPERIMENTATION

In this section, the HCCI engine basics, experimental setupand data collection strategy are described. Majority of thissection has been adopted from [8] and included in this articlefor completeness. The engine (specifications listed in Table I)is a 4 stroke, inline 4 cylinder gasoline engine with modifica-tions to enable HCCI operation, such as increased compressionratio, direct fuel injection, intake boosting and variable valvetiming. A schematic of the experimental setup and instrumen-tation is shown in Fig. 1. The sensors of the engine include afast in-cylinder pressure transducer, thermocouples at severallocations at the intake and exhaust manifold, cylinder runnersetc. The engine is operated with natural aspiration, i.e., allexperiments in this work involve no or negligible differencebetween intake and exhaust manifold pressures.

TABLE I: Specifications of the experimental HCCI engine

Engine Type 4-stroke In-lineFuel Gasoline

Displacement 2.0 LBore/Stroke 86/86 mm

Compression Ratio 11.25:1Injection Type Direct Injection

Variable Valve Timing withhydraulic cam phaser having

Valvetrain 119 degree constant durationdefined at 0.25mm lift, 3.5mm peak

lift and 50 degree crank anglephasing authority

HCCI strategy Exhaust recompressionusing negative valve overlap

A. HCCI Strategy

HCCI operation is achieved using a recompression strategy.The engine is a discrete event system where one combustioncycle (720 deg crank angle) represents an event. A snapshotof the cylinder pressure trace of one combustion cycle alongwith valve events and fuel injection events are shown in Fig. 2.During every combustion cycle, three distinct control actionscan be defined - the crank angle at intake valve opening (IVO),crank angle at exhaust valve closing (EVC) and crank angleat start of fuel injection (SOI). The valve events are measuredin degrees after exhaust top dead center (deg eTDC) whileSOI is measured in degrees after combustion top dead center(deg cTDC). It should be noted that the fuel mass (FM inmg/cyc) is injected in a region between EVC and IVO definedas the negative valve overlap (NVO). The fuel is injected early(during NVO of previous cycle) and given sufficient time tomix with air forming a homogeneous mixture. A large fractionof the exhaust gas from the previous combustion cycle (EGR)is retained to elevate the temperature and hence the reactionrates of the fuel and air mixture. The variable valve timingcapability of the engine enables trapping suitable quantitiesof exhaust gas in the cylinder. The fuel-air mixture is givensufficient time to mix homogeneously and as it is compressed


1. Coolant thermocouple 𝐶0

2. Exhaust manifold thermocouple 𝐶0

3. Exhaust manifold pressure transducer 𝑚𝑚𝑚𝑚

4. Post-turbine thermocouple 𝐶0

5. Lambda sensor −

6. Air mass flow sensor 𝑘𝑘/ℎ

7. Spark plug −

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Air in

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8. Fuel injector 𝑚𝑚𝑚𝑚

9. Cam phaser −

10, 11.

Cylinder 1 Runner T and P

𝐶0 , 𝑚𝑚𝑚𝑚𝑚

12. Intake manifold thermocouple 𝐶0

13. Intake manifold pressure transducer 𝑚𝑚𝑚𝑚

14. RPM sensor 𝑅𝑅𝑅

15. In-cylinder pressure transducer 𝑚𝑚𝑚

Throttle

Fig. 1: A schematic of the HCCI engine setup and instrumentation (only relevant instrumentation is shown).

−180 0 180 360 540 720 900 1080−5

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SOI

IVOEVC

Fig. 2: The pressure trace of a HCCI combustion cycle show-ing cycle definition, actuator ranges of intake valve opening(IVO), exhaust valve closing (EVC), start of injection (SOI).The crank angle at data recording are also shown.

during the compression stroke, auto-ignition occurs initiatingcombustion. Since the fuel is mixed homogeneously through-out the cylinder, combustion of the fuel-air mixture happensalmost instantaneously, releasing heat and pushing the pistondown performing work. More details on setup and operationof the HCCI engine can be found in [8], [10].

B. HCCI Inputs and Outputs

HCCI combustion is dominated by chemical kinetics andis limited by stability constraints such as misfire and knock[24], [25]. To achieve a stable combustion, a right proportion

of fuel, air and EGR is required for a given thermal conditionof the engine. Further, the combustion must occur at the rightinstant during the expansion stroke (given by CA50) for highefficiency and low emissions. By varying the valve events, thequantity of EGR can be varied while FM and SOI can controlthe ignition delay that affects combustion phasing. Thus, theengine operation can be controlled using quantities such asFM, IVO, EVC and SOI. Other important physical variablesthat influence the performance of HCCI combustion includeintake manifold temperature Tin, intake manifold pressure Pin,mass flow rate of air at intake min, exhaust gas temperatureTex, exhaust manifold pressure Pex, coolant temperature Tc,fuel to air ratio (FA) etc.

The engine performance metrics can be defined as follows.The indicated mean effective pressure (IMEP) represents thework output from the engine and is a primary response variableto be controlled. For instance, the driver’s power demandcan be interpreted as a change in desired IMEP commandgiven to the engine controller. The second and most importantperformance metric is the combustion phasing indicated bythe crank angle at 50% mass fraction burned (CA50). TheCA50 is a key quantity that influences engine performance,efficiency, emissions and stability [6], [7]. Further, additionalquantities that give an indication of the combustion stabilitysuch as maximum pressure (Pmax) and maximum pressure riserate (Rmax) in a combustion cycle are considered performancemetrics to be monitored. The equivalent fuel air ratio (EAFR)


that indicates if the mixture in the cylinder is fuel rich orfuel lean is another important parameter to be monitored.For HCCI control discussed in this article, the control knobssuch as FM, EVC and SOI are considered inputs whileperformance variables such as IMEP, CA50, Pmax, Rmax,engine torque and EAFR are considered outputs. The IMEP,CA50, Pmax and Rmax are calculated from the high speed in-cylinder pressure measurements. For further reading on HCCIcombustion and related variables, please refer [26], [8], [10].

C. Experiment Design

The goal of the experiments is to obtain dynamic data fromthe HCCI experimental setup for model development. Thistask falls into the category of nonlinear system identification[27]. In order to obtain sufficiently rich information from thesystem, the excitation signal must excite the system at allfrequencies and amplitudes [28]. Persistent excitation cannotbe guaranteed for nonlinear systems [28] but in practice, am-plitude modulated pseudo-random binary sequence (A-PRBS)signals have shown good identification performance [27]. Thusan A-PRBS signal exciting the engine at different amplitudesand frequencies is considered in this work. A set of transientexperiments is conducted at a constant speed of 1800 RPMand naturally aspirated conditions using a feedback controllerdeveloped for HCCI using first principles [29]. An A-PRBSsequence of reference IMEP and CA50 are given as inputsto the feedback controller while the controller calculates thecommands of FM, EVC and SOI to be given to the engine. Theexperiments are conducted and data recorded using specializedengine rapid prototyping hardware. The data is sampled usingthe AVL Indiset acquisition system where in-cylinder pressureis sensed every crank angle while IMEP, CA50, Pmax andRmax are determined on a per-combustion cycle basis. Asubset of the HCCI input and output sensor data can be shownin Fig. 3. The data is processed, scaled and converted tothe input format for ELM training. More details on HCCIcombustion, experiments and data preprocessing can be foundin [9], [8].

III. HCCI ENGINE MODEL DEVELOPMENT USINGEXTREME LEARNING MACHINES

A. Learning HCCI Dynamics using Recurrent Models

For the HCCI engine system, both the inputs and theoutputs of the engine are available as sensor measurementsand naturally, supervised learning methods can be used. TheHCCI engine is a nonlinear dynamic system and sensormeasurements represent discrete time sequences. A nonlinearauto regressive model with exogenous input (NARX) [27] canbe considered as follows

y(k) = fNARX [u(k−1), .., u(k−nu), y(k−1), .., y(k−ny)],(1)

where u(k) ∈ Rud and y(k) ∈ Ryd represent the inputs andoutputs of the system respectively, k represents the discretetime index, fNARX(.) represents the nonlinear function map-ping specified by the model, nu, ny represent the number ofpast input and output samples required (order of the system)

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Fig. 3: A subset of closed loop experimental data showing theA-PRBS inputs and the measured engine outputs.

while ud and yd represent the dimension of inputs and outputsrespectively. Let

x(k) = [u(k− 1), .., u(k− nu), y(k− 1), .., y(k− ny)]T (2)

represent the augmented input vector obtained by appendingthe input and output measurements from the system. Theengine measurement sequence can be converted to the formof training data

{(x1, y1), ..., (xN , yN )} ∈(X ,Y

)(3)

where N denotes the number of training samples, X denotesthe space of the input features (Here X = Rudnu+ydny andY = Ryd ). The above conversion of system measurements totraining data can be used to train a series-parallel model wherethe past inputs and outputs of the system (concatenated in x)is used for one-step ahead predictions (OSAP) i.e., given a setof measurements until time index k, the model predicts theoutput at time k+ 1 (see equation (4) and Fig. 4a). A parallelarchitecture on the other hand can be used to perform multiplestep ahead predictions (MSAP) by feeding back the predictionsof the OSAP model in a recurrent manner (see equation (5)and Fig. 4b). For further reading on series-parallel and parallelarchitectures, the reader is referred to [30].

y(k+1) = fNARX [u(k), .., u(k−nu+1), y(k), .., y(k−ny+1)](4)

y(k+npred) = fNARX [u(k+npred−1), .., u(k−nu+npred),

y(k + npred − 1), .., y(k − ny + npred)]. (5)

The OSAP model is used for training as existing simpletraining algorithms can be used and once the model becomesaccurate for OSAP, it can be converted to a MSAP modelrecursively in a straightforward manner. The MSAP model canbe used for making long term predictions useful for predictivecontrol discussed in section V.


(𝑥0,𝑦0)

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(𝑥1,𝑦1) (𝑥2,𝑦2) (𝑥𝑁𝑝𝑝𝑝𝑝 , 𝑦𝑁𝑝𝑝𝑝𝑝)

Model Model Model Model

(a) Series-Parallel architecture for system identification.

𝑥0 𝑥1 𝑥2 𝑥𝑁𝑝𝑝𝑝𝑝

𝑦�𝑁𝑝𝑝𝑝𝑝 𝑦0 𝑦�1 𝑦�2

Model Model Model Model

(b) Parallel Architecture for system identification.

Fig. 4

B. Extreme Learning Machines

Extreme Learning Machines is an emerging learningparadigm for multi-class classification and regression prob-lems [13], [31] and has outperformed some state of the artalgorithms such as backpropagation neural nets, support vectormachines etc. The highlight of ELM is that the training speedis extremely fast with superior generalization capabilities. Thekey enabler for ELM’s training speed is the random assign-ment of input layer parameters which do not require adaptationto the data. In such a setup, the output layer parameters can bedetermined analytically using linear least squares (See Fig. 5).Some of the attractive features of ELM include the universalapproximation capability, better generalization, the convexoptimization problem of ELM resulting in the smallest trainingerror without getting trapped in local minima, availability ofa closed form solution eliminating iterative training [13].

D

D

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Input Neurons

Hidden Neurons

Linear

Regression

Random

Projection

Output Neurons

ϕ

Wᵣ

W

ŷx

Fig. 5: Extreme learning machine model structure.

ELM training involves solving the following optimizationproblem

minW

{‖HW − Y ‖2 + λ‖W‖2

}(6)

φ = HT = ψ(WTr x(k) + br) ∈ Rnh×1 (7)

where λ represents the regularization coefficient, Y representsthe vector of outputs, ψ represents the hidden layer activationfunction (typically sigmoidal or radial basis functions) andWr,W represents the input and output layer parameters re-spectively. Here, nh represents the number of hidden neurons

of the ELM model and H represents the hidden layer outputmatrix.

A prominent feature of ELM is that the nonlinear opti-mization problem is reduced to a linear parameter estimationproblem. This reduction is made possible by the randomassignment of the input layer parameters. The matrix Wr

consists of randomly assigned elements that maps the inputvector to a high dimensional feature space while br ∈ Rnh

is a bias component assigned in a random manner similar toWr. The number of hidden neurons determine the dimensionof the transformed feature space. The random parameters canbe assigned based on any continuous random distribution [31]and remains fixed during the training process. The intuitionbehind the random parametrization of ELM can be explainedas follows. By assigning random weights as described above,along with an activation function, a regressor φ with severalfunctional combinations (with different order terms) of theinput feature vector x is obtained. For a complex problem,more hidden neurons are required which can be thought ofas introducing more complex feature mappings. When thedimension of the regressor φ is sufficiently high with sufficientinclusion of higher order (nonlinear) features, it can be mappedto the outputs linearly. Hence the training reduces to a singlestep calculation given by equation (8). The ELM decisionhypothesis can be expressed as in equation (9)

W ∗ =(HTH + λI

)−1HTY. (8)

f(x) = WT [ψ(WTr x+ br)]. (9)

C. Model Development and Validation

The engine experimental data is split into training andtesting sets. The training set consists of about 16000 cyclesof data while the testing set consists of about 7000 cycles.In order to validate multi-step ahead prediction performance,a separate MSAP-testing set containing about 2400 cycles ofdata is used. Firstly, the model hyper-parameters are tunedusing a cross-validation approach [8], [9] is employed wherea small subset of the training set is used to train the modelwith several combinations of hyper-parameters and testing itsperformance on the rest of the unseen training set. After tuningthe model hyper-parameters using cross-validation, an optimalmodel structure is determined. The optimal HCCI enginemodel consists of 20 hidden neurons with a regularization


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Fig. 6: Multi-step prediction performance of the ELM HCCI engine model. The prediction is shown in red while the actualdata is shown in blue. The corresponding model inputs (engine control inputs) such as FM, EVC and SOI are not shown asit is common to both prediction and actual data.


coefficient (λ) of 0.001 and a system order (n0) identified tobe 1. The model is retrained with the optimal hyper-parametersand evaluated on an unseen test data set. The testing andMSAP-testing data sets are never seen by the models duringtraining.

The models developed in this section are intended for usein a predictive control framework where real time predictionsare required in the engine ECU. In order to evaluate theprediction capability of the models, a root mean squared error(RMSE) given by equation (10) is used. The models are trainedusing a series-parallel architecture [30] and one-step aheadprediction performance is evaluated on the unseen testing dataset. Finally, the model predictions are evaluated for npredsteps ahead in time using a separate input sequence. Boththe testing set as well as the input sequence for multi-stepahead predictions are never seen by the model during training.This gives a good measure of the long term predictions aswell as the generalization capability of the models to unseensituations.

RMSE =

√√√√ 1

N

N∑i=1

yd∑j=1

(yij − yij)2. (10)

The test RMSE for one-step ahead prediction is observed to be0.1085 while for a 600-step ahead prediction, the test RMSEis observed to be 0.1092. The predictions are summarized inFig. 6a to Fig. 6d for different unseen MSAP-testing data sets.The RMSE values correspond to data normalized between -1and +1, and give a good indication of how well the modelcan predict the dynamics of the HCCI engine. The MSAPpredictions at several different engine operating conditions aswell as the MSAP RMSE values prove that the model can beused for predicting multiple steps ahead in time and can beused as a predictive model for the HCCI Engine in the MPCframework to be discussed in the next section IV.

IV. PREDICTIVE CONTROL FORMULATION USINGEXTREME LEARNING MACHINES

In this section, the MPC problem is formulated based ongeneral predictive control principles [15], [14] for a class ofnonlinear systems using ELM models. The formulation willbe applied to the HCCI engine problem in the later sections.

Consider a general class of nonlinear discrete time system,

z(k + 1) = f(z(k), u(k))

y(k) = g(z(k)), (11)

where z ∈ Rn, u ∈ Rm, y ∈ Rp, k the time index, n,m and prepresent the number of states, inputs and outputs respectively.f(.) and g(.) are continuously differentiable and globallyLipschitz [32] nonlinear functions modeled offline using ELM.The models can be linearized around any operating point(z0, u0) using Taylor’s series expansion as follows

z(k + 1) = f(z0(k), u0(k)) +A(z(k)− z0(k))

+B(u(k)− u0(k)) + εz,ho

y(k) = g(z0(k)) + C(z(k)− z0(k)) + εy,ho

A =

[∂f

∂z(z(k), u(k))

]z0(k),u0(k)

B =

[∂f

∂u(z(k), u(k))

]z0(k),u0(k)

C =

[∂g

∂z(z(k), u(k))

]z0(k),u0(k)

where A,B and C represent the partial derivatives of the ELMmodels in the Taylor’s expansion, εz,ho and εy,ho representhigher order terms. The linearized model can be further writtenas

z(k + 1) = Az(k) +Bu(k) + d1(k)

y(k) = Cz(k) + d2(k) (12)

d1 = f(z0(k), u0(k))− (Az0(k) +Bu0(k)) + εz,ho

d2 = g(z0(k), u0(k))− Cz0(k) + εy,ho.

The following subsections describe the calculation of the sys-tem matrices A,B and C followed by the MPC optimizationproblem formulation.

A. Calculation of System Matrices

The matrices A,B and C in equation (12) can be de-termined by exploiting the structure of the ELM model asfollows. Let the augmented input vector to ELM be given byx(k) = [u(k), z(k)]T ∈ Rn+m. The matrices A,B and C canbe determined by calculating the Jacobian of f(.) and g(.)with respect to the augmented input vector x(k). The ELMmodel structure can be expressed as

z(k + 1) = WT [ψ(WTr x(k) + br)] (13)

where ψ represents the hidden layer activation function andWr ∈ Rn+m×nh ,W ∈ Rnh×n represents the input and outputlayer parameters respectively. Here, nh represents the numberof hidden neurons of the ELM model, φ(k) = ψ(WT

r x(k) +br) ∈ Rnh×1 represents the hidden layer output matrix astermed in literature (see Fig. 5). As mentioned earlier, thematrix Wr consists of randomly assigned elements that mapsthe input vector to a high dimensional feature space whilebr ∈ Rnh is a bias component assigned in a random mannersimilar to Wr. The elements can be assigned based on anycontinuous random distribution [31] and remains fixed duringthe learning process. The number of hidden neurons determinethe dimension of the transformed feature space and the hiddenlayer is equipped with a nonlinear activation function similarto traditional neural network architecture. In this paper, asigmoidal activation function is considered.

Note that the ELM model in (13) is defined for inputsand outputs normalized to lie between [−1,+1]. Expressingthe model in (13) along with the normalization and de-normalization terms,

z(k + 1) = zmin +

(zmax − zmin

2

){1 +WTφ(k)

}φ(k) =

1

1 + e−{WT

r

[2(

x(k)−xminxmax−xmin

)−1]+br

} . (14)


Then, Jacobian matrix ∂f∂x can be derived (ignoring the time

index k) as

∂f

∂x=

(zmax − zmin

2

)WT ∂φ

∂x(15)

where

∂φi∂xj

=

2Wr(j, i)e−{WT

r,1

[2(

x−xminxmax−xmin

)−1]+br,1

}

(xmax,j − xmin,j)(

1 + e−{WT

r,1

[2(

x−xminxmax−xmin

)−1]+br,1

})2 ,

Wr,i represents the ith column of Wr and br,i represents theith element of br, ∂φ

∂x ∈ Rnh×n+m. Since the augmentedvector is defined as x(k) = [u(k), z(k)]T , the matrices A andB can be extracted from the Jacobian ∂f

∂x as[∂f

∂x

]n×n+m

= [Bn×m|An×n]. (16)

A similar jacobian calculation can be done for g(.) and also forother type of activation functions ψ(.). The above calculationsare algebraic and can be efficiently performed online.

B. MPC Optimization Problem

The goal of MPC is to force the system output y(k) track agiven reference r(k) and also penalize any large excursion inthe input signal u(k). This is obtained by solving the followingoptimization problem at every time instant k

J(k) =

Ny∑j=1

‖r(k+j|k)−y(k+j|k)‖2Q1+

Nu−1∑j=0

‖∆u(k+j|k)‖2Q2

(17)

subjected to

umin ≤ u(k + j|k) ≤ umax∆umin ≤ ∆u(k + j|k) ≤ ∆umax

ymin ≤ y(k + j|k) ≤ ymax(18)

where r(k + j|k), y(k + j|k),∆u(k + j|k) represents thereference, system output and control increment respectively.The argument (k+j|k) indicates the signal from time index kuntil k+ j being used for solving the optimization problem attime index k. Here ∆u(k+j|k) = u(k+j|k)−u(k−1+j|k),Ny and Nu are prediction horizon (Ny ≥ 1) and controlhorizon (0 < Nu ≤ Ny) respectively, ‖.‖Q1

and ‖.‖Q2denote

weighted Euclidean norm weighted by matrices Q1 and Q2

respectively. The minimum and maximum constraints for u,∆u and y are given as in equation (18).

By defining the following vectors,

Y (k) = [y(k + 1|k), y(k + 2|k), .., y(k +Ny|k)]T

∆U(k) = [∆u(k|k),∆u(k + 2|k), ..,∆u(k +Nu − 1|k)]T

R(k) = [r(k + 1|k), r(k + 2|k), .., r(k +Ny|k)]T

and calculating y(k+j|k) recursively using equation (12), thevector Y (k) can be expressed as

Y (k) = Z(k)z(k) + U(k)∆U(k) + V(k)u(k − 1)

+D1(k)d1(k) +D2(k)d2(k) (19)

where

U =

CB . . 0CB + CAB . . .

. . . .CB + .. + CANu−1B . . CBCB + .. + CANuB . . CB + CAB

. . . .CB + .. + CANy−1B . . CB + .. + CANy−NuB

V =

CB

CB + CAB..

CB + CANy−1B

,Z =

CACA2

.

.CANy

D1 =

C

C + CA..

C + CANy−1

,D2 =

IpIp..Ip

.

Q1 ∈ RNyp×Nyp, Q2 ∈ RNum×Num, Y ∈ RNyp×1,∆U ∈ RNum×1, R ∈ RNyp×1,U ∈ RNup×Num,V ∈ RNyp×m,Z ∈ RNyp×n,D1 ∈ RNyp×n,D2 ∈ RNyp×p.

The optimization problem in equation (17) can now beexpressed in vector form as

min∆U(k)

{∆Y T (k)Q1∆Y (k) + ∆UT (k)Q2∆U(k)

}(20)

where

∆Y (k) = R(k)− Y (k)

= R(k)−Z(k)z(k)− U(k)∆U(k)

−V(k)u(k − 1)−D1(k)d1(k)

−D2(k)d2(k). (21)

Expressing as a quadratic programming problem, the aboveformulation reduces to

min∆U(k)

{1

2∆UT (k)W1(k)∆U(k) +WT

2 (k)∆U(k)

}(22)

subjected to E(k) ≤ F (k) (23)

where

W1(k) = 2[UT (k)Q1U(k) + Q2]

W2(k) = −2UT (k)Q1[R(k)−Z(k)z(k)

−V(k)u(k − 1)−D1(k)d1(k)−D2(k)d2(k)]

E(k) = [INum − INum H −H U(k) − U(k)]T

F (k) =

∆Umax

−∆Umin

Umax − Uk−1

−{Umin − Uk−1}

Ymax −Z(k)z(k)− V(k)u(k − 1)−D1(k)d1(k)−D2(k)d2(k)

−{Ymin −Z(k)z(k)− V(k)u(k − 1)−D1(k)d1(k)−D2(k)d2(k)}

H =

Im 0 . . 0Im Im . . 0. . . . .. . . . .Im Im . . Im


Umin = [umin umin..umin]T

Umax = [umax umax..umax]T

∆Umin = [∆umin ∆umin..∆umin]T

∆Umax = [∆umax ∆umax..∆umax]T

Uk−1 = [u(k − 1) u(k − 1)..u(k − 1)]T

Ymin = [ymin ymin..ymin]T

Ymax = [ymax ymax..ymax]T .

Im, Ip and INum represents identity matrices in Rm×m,Rp×p and RNum×Num respectively. The above problem canbe solved using efficient quadratic programming solvers [15].The first value of the optimal control increment ∆U(k) isapplied at the present time instant k and the optimization issolved again for the next time index. This is done to handleany model inaccuracies and external disturbances.

V. APPLICATION TO CONTROL OF A GASOLINEHOMOGENEOUS CHARGE COMPRESSION IGNITION

ENGINE

The goal of this section is to design a real-time controlalgorithm that can control the HCCI engine to track a givenreference command in IMEP and CA50. The IMEP referencerepresents the driver’s load demand while CA50 reference iscalculated a priori for achieving a sweet spot between highefficiency, low emissions and stability in combustion. Theprocedure for calculating reference IMEP and CA50 is outsidethe scope of this article and the reader is referred to [33],[34]. For the controller analysis considered in this paper, it isassumed that the reference commands are available and thegoal is to determine the optimal control trajectories of FM,EVC and SOI that tracks the reference commands.

The MPC framework is shown in Fig. 7. An offline trainednonlinear model of the HCCI engine, developed using ELMin section III, is used as a proxy for the HCCI engine.At every operating point, the model is linearized and thesystem matrices are used to formulate a quadratic program asdescribed in section IV. The engine hardware limitations aswell as operating constraints are included in the optimizationproblem. The reference command includes optimal set pointsof IMEP and CA50 that is to be tracked by the engine. At everytime instant, the solver receives the present state information(z(k)) from sensor measurements and attempts several controltrajectories of FM, EVC and SOI. The optimal trajectory thatminimizes the tracking error and control excursion is given tothe engine as input.

As mentioned previously, the control knobs for the HCCIengine such as FM, EVC and SOI vary the amount of EGRtrapped in the cylinder. The EGR influences the temperatureand concentration of the mixture, affecting IMEP and CA50of the combustion event. The physical states of the system caninclude a combination of temperature, concentration, pressureof the gas mixture before combustion but a direct measurementof in-cylinder states is not feasible for production engines.In-cylinder pressure is the only available measurement fromwhich input-output models were built in section III. As a

consequence, for the control problem considered here, thestates, inputs and outputs of the system are given by

z(k) = [IMEP (k) CA50(k) Pmax(k)

Rmax(k) Tb(k) λ(k)]T ∈ R6

u(k) = [FM(k) EV C(k) SOI(k)]T ∈ R3

y(k) = [IMEP (k) CA50(k)]T ∈ R2.

The dynamic equations of the model can be expressed as in(11). This system represents a nonlinear multi-input multi-output model structure which makes control design verychallenging. Further, the engine exhibits both system leveland operation level constraints which makes traditional linearcontrol methods such as PID, LQ etc. ineffective. Further,additional challenges inherent to the HCCI engine includehigh noise amplitude levels, high sensitivity to disturbances,fast operation and tight tracking of the reference CA50. Asmentioned earlier, an MPC based approach has sufficientleeway to handle the above challenges.

MPC technology is well developed for linear systemswith computationally efficient solvers. However, application ofMPC to a nonlinear system such as the HCCI engine involvessolving a quadratic programming subproblem iteratively atevery time instant. To give an idea of the engine samplingperiod, a quadratic program problem needs to be solved every48 milliseconds when the engine operates at 2500 RPM. Thenon-availability of efficient solvers for sequential quadraticprogramming problem in real-time and the inability to guar-antee a global optimal solution for such problems constitutethe major bottleneck for nonlinear MPC techniques. However,if the system is not highly nonlinear, a linearized model canbe used to obtain suboptimal control laws in real-time usingquadratic programming. A quadratic programming is relativelymanageable than solving it sequentially for a constrainednonlinear programming problem and hence more suitable foronline applications. However, for the considered high-speedengine application, there is very little time even for a simplebut generic quadratic programming solver. In the next section,a fast quadratic programming approach is described that makesuse of the problem’s strictly convex objective function to speedup convergence.

A. Fast Quadratic Programming

The MPC problem involves solving a quadratic program-ming subproblem of the form given by equation (22). Thegeneric quadratic programming solver demands computationand memory owing to iterative interior point, active setsor trust region approximations and becomes infeasible forimplementation on the engine ECU. In order to reduce thecomputation and memory, an efficient and fast QP algorithmis adopted [35]. The algorithm can be derived as follows.

Restating the MPC quadratic programming problem from(22),

min∆U(k)

{1


2 (k)∆U(k)

}(24)

subjected to E(k)∆U(k)− F (k) ≤ 0 (25)


Linearized

ELM

Constraints

Cost

function Quadratic

Program

Offline trained

nonlinear model

HCCI

Engine

Linearization

𝑢∗ 𝑦

Fig. 7: A model predictive control framework showing the use of offline trianed nonlinear engine model for reference tracking.

where W1(k) is a symmetric positive definite matrix andthe objective function is strictly convex. The lagrangian dualproblem can be formulated as

maxλL

inf

{1


2 (k)∆U(k)

+ λL(E(k)∆U(k)− F (k))

}(26)

where λL ≥ 0. Taking the derivative with respect to ∆U ,

W1(k)∆U(k) +W2(k) + ET (k)λL = 0. (27)

The dual problem can be expressed as

maxλL

{1


2 (k)∆U(k)

+ λL(E(k)∆U(k)− F (k))

}(28)

subjected to

W1(k)∆U(k) +W2(k) + ET (k)λL = 0

y ≥ 0.

Since W1(k) is positive definite, W1(k)−1 exists and equation(27) can be solved as follows

∆U∗ = −W1(k)−1(W2(k) + ET (k)λL). (29)

Following a direct substitution of (29) in (28), the problembecomes

maxλL

{1

2λTLΛ1λL + λTLΛ2 −

1

2WT

2 (k)W−11 (k)W2(k)

}(30)

subjected to y ≥ 0 (31)

where Λ1 = −E(k)W−11 (k)ET (k) and Λ2 = −F (k) −

E(k)W−11 (k)W2(k). The problem in (30) can be solved using

a simple gradient ascent method as follows.

λLk+1= λLk

+ λstep(Λ1λL + Λ2). (32)

In order to satisfy the constraint in (31), the following modi-fication is made

λLk+1= max(λLk

+ λstep(Λ1λL + Λ2), 0) (33)

where λstep defines the step size. The solution of (33) gives theoptimal λ∗L which can be substituted in (29) to get the optimalMPC output ∆U∗. The strictly convex property of the MPCproblem is made use of in solving the quadratic programmingsubproblem efficiently.

B. Simulation Setup

For the study considered here, the offline trained nonlinearmodel is considered as the true HCCI engine plant for whichthe MPC controller is designed. The goal of the controller is totrack the reference IMEP and CA50 trajectories with minimumerror and with minimum change in control input (see (17)).The reference trajectory is designed offline depending on theallowable operating regions of HCCI and the valid region ofthe HCCI engine model. The step references are designed tovary between 2.6 and 3.2 bar IMEP and between -4 and -10deg CA50 defined in degrees before combustion TDC. Thiscovers most of the naturally aspirating HCCI operating rangeat 1800 RPM. The MPC constraints are defined as follows.It should be noted that the objective function and constraintscan be modified in a straightforward manner to include moreperformance metrics such as emissions, combustion roughness,knock levels etc.

umin = [19 − 121 272]T

umax = [25 − 100 375]T

∆umin = [−6 − 22 − 103]T

∆umax = [6 22 103]T

ymin = [2.1 − 14]T

ymax = [3.55 − 2]T .

C. High Amplitude Noise of HCCI

As mentioned earlier, combustion phasing is an importantquantity that indicates engine performance. Combustion is not


−10 0 100

50

100

150IMEP =3.26

−5 0 50

10

20

30

40IMEP =3

−5 0 50

5

10

15IMEP =2.63

−5 0 50

10

20

30

40IMEP =2.88

−0.1 0 0.10

5

10CA50 =−8.93

−0.2 0 0.20

5

10

15

20CA50 =−7.45

−0.2 0 0.20

5

10

15CA50 =−7.87

−0.2 0 0.20

10

20

30

40CA50 =−8.55

Fig. 8: Noise characteristics of CA50 (top rows) and IMEP (bottom rows) as observed in the HCCI engine experimental datafor different operating conditions.

an instantaneous process but extends over a period of time.Significant research has been done in determining an appro-priate parameter that summarize the combustion event andthat has good indication over phasing [6], [7]. It was widelyaccepted that CA50 was a robust indicator for combustionphasing. However, CA50 is characterized by a highly randomprocess involving noise in the in-cylinder pressure measure-ments, variability in gas mixing, heat transfer, difference incylinder-to-cylinder design and cycle-to-cycle variations [2],[24], [6]. As a consequence, the variability in CA50 is high.The IMEP is a more averaged effect of the pressure charac-teristics in the cylinder and thus its variability is lesser. Thenoise distribution of IMEP and CA50 at certain representativeoperating conditions are summarized in Fig. 8. It can be seenthat the noise is almost Gaussian with zero mean. The top rowsrepresent noise in CA50 signals at different IMEP conditionswhile the bottom rows represent noise in IMEP measurementsat different CA50 conditions. The MPC framework consideredin this work involves linearization of the models at everyoperating point defined by sensor measurements. In orderto simulate the controller’s robustness to the high amplitudenoise seen in HCCI engine measurements, white noise signalsof zero mean and variances 0.0012 and 1.76 are injectedat the outputs of the IMEP and CA50 model respectivelyand the models are linearized around the noisy measurementsexperienced in real engine operation.

D. Results And Discussion

In this section, the results of the ELM based MPC resultsare summarized. A simulation is conducted with a Matlab real-time target bypassing communication with the engine ECU.The ELM model is observed to compactly represent the HCCI

engine with about 320 parameters (Wr ∈ Rn+m×nh , br ∈Rnh ,W ∈ Rnh×n). This compactness in comparison to earlierneural network and SVR models is significant [8], [9] forthe MPC application. Further, the fast quadratic programmingapproach enabled online implementation of the MPC. At everysimulation step, the inputs and outputs of the engine modelare available as sensor measurements to the MPC system. TheHCCI model is linearized around sampled states and is usedin the online MPC algorithm to determine the optimal controlincrement (∆U∗), i.e., the optimal fuel mass, EVC and SOI tobe given to the engine to track the reference commands. Afterperforming several trial and error simulations, the predictionand control horizons take values Ny = 3 and Nu = 3, tunedfor minimum tracking error. Similarly, the gain matrices aretuned to be

Q1 =

500 0 0 0 0 00 1 0 0 0 00 0 500 0 0 00 0 0 1 0 00 0 0 0 500 00 0 0 0 0 1

Q2 =

20 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 00 0 1 0 0 0 0 0 00 0 0 20 0 0 0 0 00 0 0 0 1 0 0 0 00 0 0 0 0 1 0 0 00 0 0 0 0 0 20 0 00 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 1

.

The odd diagonal values of Q1 correspond to reducing IMEPtracking error while the even diagonal values correspond to


0 500 1000 1500 2000

2.8

3

IME

P(b

ar)

Tracking performance

System StateReference

0 500 1000 1500 2000−10

−5

CA

50(d

eg b

TD

C) Tracking performance

0 500 1000 1500 200030

35

40

Pm

ax(b

ar)

0 500 1000 1500 2000

2

3

4

Rm

ax(b

ar/d

eg)

0 500 1000 1500 2000

25

30

Tor

que

(Nm

)

0 500 1000 1500 2000

1.21.25

1.3

EA

FR

(−)

Combustion Cycles

(a) State trajectories of the HCCI engine model (with noise) using MPC control(case 1: constraint on Rmax not enforced in the MPC formulation).

0 500 1000 1500 2000

20

22

24

Fue

l Mas

s(m

g/cy

c)

0 500 1000 1500 2000

−120

−115

−110

−105

−100

Exh

aust

Val

ve C

losi

ng(d

eg a

CT

DC

)0 500 1000 1500 2000

340

345

350

Sta

rt o

f Inj

ectio

n(d

eg a

ET

DC

)Combustion Cycles

(b) Control trajectories of the HCCI engine model (with noise) using MPCcontrol (case 1 constraint on Rmax not enforced in the MPC formulation).The upper and lower limits of each actuator is shown in dotted red.

0 500 1000 1500 2000

2.8

3

IME

P(b

ar)



0 500 1000 1500 2000−10

−5

CA

50(d

eg b

TD


0 500 1000 1500 200030

35

Pm

ax(b

ar)

0 500 1000 1500 2000

2

3

4

Rm

ax(b

ar/d

eg)

0 500 1000 1500 2000

242628

Tor

que

(Nm

)

0 500 1000 1500 20001.15

1.21.25

1.3

EA

FR

(−)

Combustion Cycles

(c) State trajectories of the HCCI engine model (with noise) using MPC control(case 2 constraint on Rmax enforced in the MPC formulation).

0 500 1000 1500 2000

20

22

24

Fue

l Mas

s(m

g/cy

c)

0 500 1000 1500 2000

−120

−115

−110

−105

−100

Exh

aust

Val

ve C

losi

ng(d

eg a

CT

DC

)

0 500 1000 1500 2000

330

335

340

345

350

Sta

rt o

f Inj

ectio

n(d

eg a

ET

DC

)

Combustion Cycles

(d) Control trajectories of the HCCI engine model (with noise) using MPCcontrol (case 2 constraint on Rmax enforced in the MPC formulation). Theupper and lower limits of each actuator is shown in dotted red.

Fig. 9: Evaluation of MPC controller using HCCI engine simulator.


reducing CA50 tracking error. The relative difference in valuesbetween IMEP and CA50 indicates the relatively high noiselevel of CA50 and a smaller weight trying to track the noisyCA50 less aggressively. Q2 is tuned to avoid saturation of theinput signals (taken as constraints in the MPC formulation).The gain corresponding to FM is high indicating a largeexcursion in FM is penalized so that fuel mass is slowly varied.This is done to ensure that both FM and SOI from reachingtheir actuator limits.

To evaluate the MPC performance, a reference commandinvolving a series of random steps of IMEP and CA50 isconsidered. The step input to the controller can be thoughtof as shifting the engine from one set point to another andgives a good idea of the control performance in terms ofresponse speed, transient and steady state performances. It canbe observed from Fig. 9a that the controller is able to trackthe considered reference. The time taken by the controller toswitch the engine from one set point to the next is about 5cycles for a small step to about 20 cycles for a large step. Bytuning the MPC gains further, the transients of the controllercan be shaped to tradeoff between quickness in response toovershoot and minimum oscillations around the reference.Care must be taken while tuning the gains so that the controllerdoes not saturate the actuators or violate the constraints. Alsofrom Fig. 9a, the transients of the other states of the engineincluding Pmax, Rmax, engine brake torque and fuel richnessin the mixture can be observed. These quantities are obtainedfrom the HCCI engine model for the optimal MPC controltrajectories. The control inputs (optimal trajectories) of MPCsuch as FM, EVC and SOI can be seen in Fig. 9b. It can beobserved that none of the actuators violate the specified limits.

In the above simulation, the constraints are specified onlyfor the actuators and output variables such as IMEP and CA50.However in real situations, typically the engine operation isconstrained between stability limits such as misfire, knockand ringing. In order to analyze MPC performance with stateconstraints and stability limits, an additional constraint isdefined on Rmax. In Fig. 9a, the maximum rate of pressurerise (Rmax) exceeds 3.5 bar/deg CA(shown by red dotted line).By including this as a state constraint in the MPC formulation,the second simulation is performed. The MPC performanceis summarized in Fig. 9c and Fig. 9d. It can be observedthat the MPC control is modified so that the engine Rmaxis less than 3.5 bar/deg CA. A direct comparison of the MPCcontrol trajectories in Fig. 9b and Fig. 9d shows that when theconstraint on Rmax is active, MPC reduces the SOI commandto operate the engine with less pressure rise rates for the givenIMEP and CA50 reference commands. This summarizes thecapability of the proposed approach to compute a solutionfor the multi-input multi-output control problem in an optimalmanner. It has to be noted that, as the constraint is active, itbecomes difficult for MPC to achieve close tracking as theavailable freedom is restricted by the active constraint. Bytuning the gains further, a better tracking may be achieved.

Finally, in order to simulate the engine demands in a vehicleapplication, a slowly varying sinusoidal reference commandis given both for IMEP and CA50. This is to simulate theengine power demand while accelerating and slowing down

repeatedly. The control performance is summarized in Fig.10a and Fig. 10b. It can be observed that the MPC tracks thegiven reference to a good degree of accuracy with constraintsatisfaction. Hence, the above simulation cases demonstratethe working of ELM based MPC, its manageable computa-tional complexity and its overall potential for real time HCCIengine control.

VI. CONCLUSIONS AND FUTURE WORK

HCCI engine control is a nonlinear, multi-input multi-outputproblem with state and actuator constraints which calls foradvanced control designs. In this paper, a model predictivecontrol approach has been demonstrated that tracks multiplereference quantities along with constraints on HCCI states andcontrol inputs.

A nonlinear system identification is performed using ex-treme learning machines and HCCI engine models are de-veloped using experimental data. ELM models are shown tocompactly represent the nonlinear dynamics of HCCI and canbe used for predicting several steps ahead of time for opti-mization purposes. An analytical derivative calculation usingthe structure of ELM models is used which can avoid issuesassociated with numerical derivatives. The MPC optimizationis formulated as a convex problem for which a fast quadraticprogramming method is used. Simulation studies have beenconducted to demonstrate the working of ELM based MPCfor the considered HCCI engine problem.

In summary, this article demonstrates a computationallyfeasible approach to perform MPC for HCCI engines usinga nonlinear model in real-time. Future work would focus onextending the method to develop controller for the experimen-tal engine and reformulating MPC to include vehicle levelobjectives such as fuel economy and emissions.

ACKNOWLEDGMENT

This material is based upon work supported by the De-partment of Energy and performed as a part of the ACCESSproject consortium (Robert Bosch LLC, AVL Inc., EmitecInc.) under the direction of PI Hakan Yilmaz, Robert Bosch,LLC. X. Nguyen is supported in part by NSF Grants CCF-1115769 and ACI-1047871.

DISCLAIMER

This report was prepared as an account of work sponsoredby an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor any oftheir employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus,product, or process disclosed, or represents that its use wouldnot infringe privately owned rights. Reference herein to anyspecific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise does not nec-essarily constitute or imply its endorsement, recommendation,or favoring by the United States Government or any agencythereof. The views and opinions of authors expressed hereindo not necessarily state or reflect those of the United StatesGovernment or any agency thereof.


0 500 1000 1500 20002.62.8

33.2

IME

P(b

ar)



0 500 1000 1500 2000−10

−5

CA

50(d

eg b

TD


0 500 1000 1500 200030

35

Pm

ax(b

ar)

0 500 1000 1500 2000

2

3

4

Rm

ax(b

ar/d

eg)

0 500 1000 1500 2000

25

30

Tor

que

(Nm

)

0 500 1000 1500 2000

1.2

1.3

EA

FR

(−)

Combustion Cycles

(a) State trajectories of the HCCI engine model (with noise) using MPC control(case 3: sinusoidal reference commands).

0 500 1000 1500 2000

20

22

24

Fue

l Mas

s(m

g/cy

c)

0 500 1000 1500 2000

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)

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f Inj

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DC

)Combustion Cycles

(b) Control trajectories of the HCCI engine model (with noise) using MPCcontrol (case 3: sinusoidal reference commands). The upper and lower limitsof each actuator is shown in dotted red.

Fig. 10: Evaluation of MPC controller using HCCI engine simulator.

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Vijay Manikandan Janakiraman received thebachelor’s degree in Mechanical Engineering (2007)from Sri Venkateswara College of Engineering,Chennai, India. He received Master’s degrees inMechanical Engineering (2008) and Electrical En-gineering - Systems (2013) and the Ph.D. degree inMechanical Engineering (2013) from the Universityof Michigan at Ann Arbor, MI, USA.

Since August 2013, he has been working as aresearch scientist with the Data Sciences Group,Intelligent Systems Division at the NASA Ames

Research Center, Moffett Field, CA, USA. His current research interestsinclude machine learning, data mining in high dimensional time series,dynamical systems, optimization and control.

XuanLong Nguyen received the Ph.D. degree incomputer science and the M.S. degree in statistics,both from the University of California, Berkeley.He is currently an Assistant Professor of Statis-tics at the University of Michigan. His researchinterests lie in distributed and variational inference,nonparametric Bayesian statistics, and applicationsto detection/estimation problems in distributed andadaptive systems. Dr. Nguyen is a recipient of theCAREER award from the NSF Division of Mathe-matical Sciences, the Leon O. Chua Award from the

UC Berkeley, the IEEE Signal Processing Societys Young Author Best Paperaward, and an Outstanding Paper award from the International Conference onMachine Learning.

Dennis Assanis received the Ph.D. degree in Powerand Propulsion and the M.S. degrees in Naval Ar-chitecture and Marine Engineering and Mechani-cal Engineering from the Massachusetts Instituteof Technology. Dr. Assanis is a Professor in theDepartment of Mechanical Engineering and is alsothe Provost, Senior Vice President for AcademicAffairs, and Vice President for Brookhaven Affairsat the Stonybrook University, NY, USA. Assanisserved as the Jon R. and Beverly S. Holt Professor ofEngineering and Arthur F. Thurnau Professor at the

University of Michigan, as well as Director of the Michigan Memorial PhoenixEnergy Institute, Founding Director of the US-China Clean Energy ResearchCenter for Clean Vehicles and Director of the Walter E. Lay AutomotiveLaboratory. Dr. Assanis research interests lie in the thermal sciences andtheir applications to energy conversion, power and propulsion, and automotivesystems design. His research focuses on analytical and experimental studies ofthe thermal, fluid and chemical phenomena that occur in internal combustionengines, after-treatment systems, and fuel processors. His efforts to gain newunderstanding of the basic energy conversion processes have made significantimpact in the development of energy and power systems with significantlyimproved fuel economy and dramatically reduced emissions. His groupsresearch accomplishments have been published in over 250 articles in journalsand international conference proceedings. Dr. Assanis is a Member of theNational Academy of Engineering and is an ASME and SAE Fellow.

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