LCCC Workshop: Systems Design meets Equation-based Languages

19-21 September 2012

Old Bishops Palace at Biskopsgatan 1 in Lund

Scientific CommitteeJohan kesson, Lund University, Sweden (Chair)

Moritz Diehl, KU Leuven, BelgiumHilding Elmqvist, Dassault Systmes, Sweden

Claus Fhrer, Lund University, SwedenClas Jacobson, United Technologies Research Center, USA

Eric Van Wyk, University of Minnesota, USAAnders Rantzer, Lund University, Sweden, LCCC coordinator

Organizing CommitteeClaus FhrerGrel Hedin

Anders RantzerEva Westin

Johan kesson

MAILING ADDRESSDepartment of Automatic ControlLund UniversityBox 118SE-221 00 LUND, SWEDEN

VISITING ADDRESSInstitutionen fr ReglerteknikOle Rmers vg 1232 63 LUND

TELEPHONE+46 46 222 87 87

FAX+46 46 13 81 18

GENERIC E-MAIL ADDRESScontrol@control.lth.se

WWWwww.lccc.lth.se

Printed: Media-Tryck, Lund, Sweden, August 2013

ISSN 0280-5316ISRN LUTFD2/TFRT--7638--SE

3

Content

1. Introduction 51.1 Workshop Theme 51.2 Scope 51.3 Organization and venue 62. Panel discussion 72.1 Modeling and systems engineering in education 72.2 Employing equation-based languages in systems design 72.3 Formalization of models 83. Summary and outlook 93.1 Important observations 93.2 Open problems 93.3 Actions 10

Appendix A PROGRAM 11

Appendix B PARTICIPANTS 13

Appendix C PRESENTATIONS 15Non-standard semantics of hybrid systems modelers 15Albert Benveniste, IRISA/INRIA

Equations, Synchrony, Time, and Modes 30Edward A. Lee, EECS, UC Berkeley

Formal Modeling and Analysis of Software Systems with Lustre 39Mike Whalen, University of Minnesota

Systems Engineering: Status of Industrial Use, Opportunities and Needs 46Clas Jacobson, United Technologies Systems & Controls Engineering

The OpenModelica Environment including Static and Dynamic Debugging of Modelica Models and Systems Engineering/Design verification 51Peter Fritzson, Linkping University, Department of Computer and Information Science, PELAB Programming Environment Laboratory

The Dark Side of Object-Oriented Modelling: Numerical Problems, Existing Solutions, Future Perspectives 65Francesco Casella, Politecnico di Milano, Dipartimento di Elettronica e Informazione

Bridging between different modeling formalisms results from the MULTIFORM project 75Sebastian Engell, Process Dynamics and Operations Group, Department of Biochemical and Chemical Engineering, TU Dortmund

Equation-based Modeling and Control of Industrial Processes 84Johan Sjberg, ABB AB, Corporate Research and Linkping university

FMI: Functional Mockup Interface for Model Exchange and Co Simulation 91Torsten Blochwitz, ITI GmbH Dresden, Germany

4

Vertical Integration in Tool Chains for Modeling, Simulation and Optimization of Large-Scale Systems 102Johan kesson, Modelon AB and Lund University, Lund, Sweden

System Design From Requirements to Implementation 109Alberto Ferrari, ALES S.r.l.

Synchronous Control and State Machines in Modelica 116Hilding Elmqvist, Dassault Systmes AB

Extensible Programming and Modeling Languages 126Eric Van Wyk, University of Minnesota

Extensible compiler architecture examples from JModelica.org 133Grel Hedin, Dept of Computer Science, Lund University, Sweden

Constraint satisfaction methods in embedded system design 138Krzysztof Kuchcinski, Dept. of Computer Science, Lund University

Dynamical models for industrial controls: use cases and challenges 148Fernando DAmato, GE Global Research Cente

Origins of Equation-Based Modeling Languages 155Karl Johan strm, Department of Automatic Control, LTH, Lund University Lund, Sweden

Assimulo a Python package for solving differential equation with interface to equation based languages 163Claus Fhrer, Centre of Mathematical Sciences, Lund University

CasADi: A Tool for Automatic Differentiation and Simulation-Based Nonlinear Programming 169Moritz Diehl, Electrical Engineering Department and Optimization in Engineering Center OPTEC KU Leuven

Pyomo: Optimization Modeling in Python 182Carl Laird, Artie McFerrin Department of Chemical Engineering, Texas A&M University

Efficient symbolical and numerical algorithms for nonlinear model predictive control with OpenModelica 195Bernhard Bachmann, Fachhochschule Bielefeld University of Applied Sciences

Modeling Seen as Programming 210Klaus Havelund, Jet Propulsion Laboratory, California Institute of Technology

Verification of Stiff Hybrid Systems by Modeling the Approximations of Computational Semantics 232Pieter J. Mosterman, MathWorks

Algorithmic differentiation: Sensitivity analysis and the computation of adjoints 253Andrea Walther, Institut fur Mathematik Universitt Paderborn

Functional Development with Modelica 270Stefan-Alexander Schneider, Schneider System Consulting

5

1. Introduction

LCCC workshops are organized in a 3-day for-mat. About 20-25 speakers from academia and industry are invited for the workshop, selected for excellence and for an optimal coverage of the theme. The speakers are also encouraged to extend their stay beyond the workshop for further interaction with the local research en-vironment. For each workshop, the research theme is chosen strategically to support the vision of a LCCC, usually with a cross-disciplinary perspective. An international scientific commit-tee is responsible for the program.

1.1 WORKSHOP THEMEEquation-based object-oriented languages (EOOL), such as Modelica and VHDL-AMS, have become widely used in academia and industry during recent years. While these languages are mainly oriented towards dynamic simulation, they are well suited as a basis for solving a wider range of engineering design problems, making use of existing and new algorithms. Examples include sensitivity analysis, state and parameter estimation, optimal control and MPC, robust design, and model reduction.

1.2 SCOPE The workshop focused on how EOOLs can be extended to support this wider range of pro-blems in systems design. The following aspects are of primarily interest:

1. Extension examples: What kind of engine-ering design problems could benefit from support through EOOLs, or extensions to an EOOL language? What existing or new al-gorithms could be used for such extensions? An existing example for such an extension is Optimica which adds optimization capabili-ties to Modelica.

2. Language extension design: How can such

extensions be formulated as language ex-tensions? What different techniques, e.g., annotations, syntactic extensions, semantic extensions, or embedded DSLs are appropri-ate for different extensions? How can model execution standards, e.g., the Functional Mock-up Interface (FMI) be explored to link language extensions to algorithms?

3. Language extension implementation: How can these extensions be implemented in supporting tools like compilers? How can modularity with respect to core languages be maintained? How can interactive tools like IDEs be extended to support the language extensions? Examples of new metacompila-tion frameworks supporting language exten-sions include JastAdd, Silver, and Kiama.

4. Applications: What interesting industrial cases can be found that could benefit from such new developments?

Supporting such extensions to EOOLs would answer the strong industrial need for integra-ting existing EOOL models with systems design algorithms and on-line control systems.

The problems are cross disciplinary, and the aim of the workshop was therefore to bring to-gether researchers and industrial practitioners in several fields, including engineering design (modeling, simulation, optimization, etc.), com-puter science (languages and tools), numerical analysis (algorithms for solving design problems), and applications.

The workshop supported the LCCC theme Modeling for design and verification. During the last few years, a local community has emerged, consisting of researchers at the departments of Mathematics, Computer Science and Automa-tic Control, and companies, notably Modelon, Lund, and ABB, Malm. The local community is oriented towards the two open source projects

6 INTRODUCTION

JModelica.org (an open-source implementation of Modelica) and JastAdd (a meta-compilation tool supporting language extension). The theme of the workshop stemmed from this environ-ment cross-disciplinary interactions between researchers at Lund university, local companies, and students are frequent. Such interactions include joint masters thesis projects, joint sci-entific publications, joint PhD student advising, all inspired by industral applications.

1.3 ORGANIZATION AND VENUEThe workshop was initiated by Claus Fhrer (Center for Mathematical Sciences), Grel Hedin (Department of Computer Science) and Johan kesson (Department of Automatic Control).

The scientific committee consisted of Johan kesson (chair), Moritz Diehl, Hilding Elmqvist, Claus Fhrer, Clas Jacobson and Eric van Wyk.

The local organization and interactions with workshop speakers and participants was hand-led by Eva Westin.

The workshop was held at the Pufendorf Insti-tute at Lund University 19-21 September 2012.

7

2. Panel discussion

Participants: Albert Benveniste, Hilding Elmqvist, Carl D. Laird, Edward E. Lee, Clas Jacobson

Moderator: Karl Johan strm

The panel discussion circled around three main themes; modeling and systems engine-ering in eduction, employing equation-based languages in systems design, and formaliza-tion of model representations.

2.1 MODELING AND SYSTEMS ENGINEERING IN EDUCATIONC. Jacobson put forward the observation that systems engineering is no longer taught by academic institutions. As a consequence, graduated engineers lack experience with systems design tools, which are widely used in industry. In cases where systems design courses are offered by universities, they are often taught by industrial practitioners that are brought in for the occasion.

E. Lee suggested to introduce a new topic into program curricula: Model Engineering. While this topic would build on established disciplines, it would emphasize that the con-cept of modeling as a key element in systems engineering. What is currently offered by universities in this area is generally weak. E. Lee made an analogy to software engine-ering, which has a long-time tradition within academia, and which contains a number of structured concepts that are taught systema-tically. Concepts suggested to be integrated into the topic model engineering include object-orientation, represented by languages such as Modelica, and refactoring of model code, which is a standard technique in soft-ware engineering.

A. Benveniste noted that mathematics is and must remain a fundamental element of systems engineering mathematics is every-

where! It was also noted that French software industry emphasizes systems engineering for this particular reason.

2.2 EMPLOYING EQUATION-BASED LANGUAGES IN SYSTEMS DESIGNIn his opening note, H. Elmqvist talked about recent directions in the development of the Modelica language. The latest version of Modelica supports synchronous constructs. State-machines have been added in order to promote modeling of clock and sequential control systems. H. Elmqvist stressed the need to continue to expand the scope of Modelica to cover areas such as requirements mana-gement, integration with 3D modeling tools, Monte Carlo analysis, embedded optimization in physical models and systems design in ge-neral. H. Elmqvist also took the opportunity to invite everybody to interact and to contribute to the further development of Modelica.

C. Jacobson commented that equation-based languages are currently not used to their full potential. Given the languages and tools available today, we can move from ex-perimentation based on simulation to compu-tations in systems design. C. Jacobson men-tioned Six Sigma and Monte Carlo techniques as targets for integration with computational frameworks based on physical models, and he highlighted rich opportunities for research in the area, for example in propagation of uncertainty.

C. Laird talked about the interplay between algorithm design and modeling, specifially in the context of dynamic optimization of large-scale non-linear systems. In effect, the way models are constructed is affected by the ca-pabilities of such algorithms. In addition, the need for exploitation of structure in models was stressed.

8 PANEL DISCUSSION

2.3 FORMALIZATION OF MODELSA. Benveniste used the fighter aircraft Rafale to exemplify the need for integrated and formal methods in requirements managment and veri-fication. Approximately 250.000 requirements were considered in the design. The process was characterized by informal handling of the requi-rements, multiple engaged sub-contractors, and often, requirements verification without mo-dels. In other activities in the project, however, models were developed and used extensively, including system dimensioning, control design and Product Lifecycle Management (PLM). Typi-cally, very different modeling tools were used for these purposes. Based on the example, A. Ben-veniste put forward questions to be adressed in research and in industrial practice. How to fuse the model-based tools in order for models to become widely available in different processes? How does the V-model for product development come into play in this context? What is needed in terms of Modelica extensions in order to ac-comodate the needs exemplified in the Rafale project?

In his remarks, E. Lee reasoned about what properties of models we should value. Three aspects were brought forward. Firstly, fidelity of models is a key property, that is to what de-gree the models mimic a given system. Secondly, understandability of a model, something we are often eager to sacrifice, should be valued. E. Lee called for a cultural change in this respect we should be proud of small models! Thirdly, analyzability of a model is important in order to perform model-based analyses such as model checking and verification. E. Lee stressed in this context the need for formal model description formats.

9

3.1 IMPORTANT OBSERVATIONS Different approaches to modeling of hybrid

systems were discussed during the work-shop. This seems to be one of the core chal-lenges in the area, i.e., to develop a rigorous mathematical formalism to describe the semantics of models encoded in languages such as Modelica, Ptolemy and VHDL-AMS, and in model exchange standards such as FMI.

The interest in model exchange formats which are neutral with respect to physical domain, modeling language, and software tool is increasing. The Functional Mock-up Interface is rapidly being adopted in research and in industry, which was evident from se-veral presentations. In addition, the CIF for-mat which resulted from the MULTIFORMS project was presented.

The interest in Modelica is broadening, and the scope of the language is expanding from primarily modeling of physical systems to control systems and systems design. Speci-fically, synchronous extensions to Modelica and optimization based on Modelica models were discussed. Also, the potential of Mo-delica in systems design was high-lighted during the panel discussion.

The need for formal verification of require-ments, and approaches to solving such pro-blems was a strong theme during the work-shop. This topic was high-lighted during the panel discussion in the context of aircraft control systems and in several presentations.

Some speakers bore witness to difficulties in applying software for non-convex dynamic optimization to industrial problems. The level of maturity of existing algorithms for such problems seems to be significantly less than

3. Summary and outlook

for simulation tools targeting the same class of systems.

Extensible languages and compilers is beco-ming feasible through research efforts in the computer science community. Two different approaches to compiler extensibility was dis-cussed in the workshop presentations.

Python holds a strong position in the scien-tific computing field, which was underlined in a number of presentations.

3.2 OPEN PROBLEMS Modeling formalizms for hybrid systems.

Several speakers touched upon modeling for-malisms for hybrid systems. While there are different frameworks available for descrip-tion of hybrid systems, consensus is yet to be reached upon the semantic behaviour and a unified mathematical theory.

Robustness of numerical optimization algorithms for large-scale non-linear dnamic systems. The academic community has produced a large body of algorithms for optimization of large-scale non-linear dy-namic systems. Still, industrial practitioners experiences significant challenges in apply-ing such algorithms to problems relevant for their applications.

Physical modeling languages for convex optimization. Current modeling languages such as VHDL-AMS and Modelica target con-struction of non-linear and hybrid physical system models, which are not immediately useful as a basis for the large body of availa-ble optimization algorithms for convex opti-mization. Still, many physical systems can be modeled in order to fulfill the requirements of convex optimization. Accordingly, chal-lenges remain in combining concepts from EOOL and convex optimization.

10 SUMMARY AND OUTLOOK

3.3 ACTIONSFrom the discussions during the workshop, it is clear that there are rich opportunities for cross fertilization between different fields represen-ted by speakers and paricipants. Based on these discussions, the following actions are recom-mended.

More efforts are needed in terms of language support for optimization. Several presentations touched upon this topic and several interesting directions were mentioned, including convex optimization formulations based on physical modeling languages, challenges in application of state-of-the-art optimization algorithms to large-scale physical models, and industrial applications.

Increased interaction is needed between communities working with modeling for-malisms for hybrid systems. It is clear that there are several research groups developing modeling formalisms for hybrid systems, as well as industrial initiatives such as FMI and Modelica. Interactions between these groups would be beneficial in order to develop a unified framework for modeling of hybrid sys-tems. An initiative in this direction was taken by the Modelica community, represented by H. Elmqvist, who visited E. Lees group in the weeks following the workshop.

Establishment of a repository of dy-namic benchmark models of industrial grade to support research in systems design. Development of relevant industrial grade models requires a high level of exper-tise, that this not always available in research projects targeting systems design. Such pro-jects benefit from freely available dynamic models.

11PANEL DISCUSSION

Wednesday, September 19, 2012

08.30-09.00 Registration09.00-09.10 Opening session09:10-10:10 Non-standard semantics of hybrid systems modelers Albert Benveniste, IRISA/INRIA Equations, Synchrony, Time, and Modes Edward A. Lee, EECS, UC Berkeley10:10-10:40 Coffee10:40-12:10 Formal Modeling and Analysis of Software Systems with Lustre Mike Whalen, University of Minnesota Systems Engineering: Status of Industrial Use, Opportunities and Needs Clas Jacobson, United Technologies Systems & Controls Engineering The OpenModelica Environment including Static and Dynamic Debugging of Modelica Models and Systems Engineering / Design verification Peter Fritzson, Linkping University, PELAB12:10-13:30 Lunch13:30-15:00 The Dark Side of Object-Oriented Modelling: Numerical Problems, Existing Solutions, Future Perspectives Francesco Casella, Politecnico di Milano Bridging between different modeling formalisms results from the MULTIFORM project Sebastian Engell, TU Dortmund Equation-based Modeling and Control of Industrial Processes Johan Sjberg, ABB AB, Corporate Research and Linkping university15:00-15:30 Coffee15:30-16:30 FMI: Functional Mockup Interface for Model Exchange and Co-Simulation Torsten Blochwitz, ITI GmbH Dresden Vertical Integration in Tool Chains for Modeling, Simulation and Optimization of Large-Scale Systems Johan kesson, Modelon AB and Lund University

Thursday, September 20, 2012

09:00-10:00 System Design From Requirements to Implementation Alberto Ferrari, ALES S.r.l. Synchronous Control and State Machines in Modelica Hilding Elmqvist, Dassault Systmes AB10:00-10:30 Coffee

Appendix A PROGRAM

12 PANEL DISCUSSION

10:30-12:00 Extensible Programming and Modeling Languages Eric Van Wyk, University of Minnesota Extensible compiler architecture examples from JModelica.org Grel Hedin, Lund University Constraint satisfaction methods in embedded system design Krzysztof Kuchcinski, Lund University12:00-13:30 Lunch13:30-15:00 Discussion15:00-15:30 Coffee15:30-16:30 Dynamical models for industrial controls: use cases and challenges Fernando DAmato, GE Global Research Center Origins of Equation-Based Modeling Languages Karl Johan strm, Lund University18:20 Gathering at Bangatan 14 (next to Ica Kvantum Malmborgs)19:00 Workshop dinner at Hckeberga castle

Friday, 21 September, 2012

09:15-10:00 Panel discussion10:00-10:30 Coffee10:30-12:00 Pyomo: Optimization Modeling in Python Carl Laird, Texas A&M University Efficient symbolical and numerical algorithms for nonlinear model predictive control with OpenModelica Bernhard Bachmann, Fachhochschule Bielefeld University of Applied Sciences Algorithmic differentiation: Sensitivity analysis and the computation of adjoints Andrea Walther, Universitt Paderborn12:00-13:00 Lunch13:00-14:30 CasADi: A Tool for Automatic Differentiation and Simulation-Based Nonlinear Programming Moritz Diehl, OPTEC KU Leuven Modeling Seen as Programming Klaus Havelund, Jet Propulsion Laboratory, California Institute of Technology Verification of Stiff Hybrid Systems by Modeling the Approximations of Computational Semantics Pieter J. Mosterman, MathWorks14:30-15:00 Coffee15:00-16:00 Assimulo a Python package for solving differential equation with interface to equation based languages Claus Fhrer, Lund University Functional Development with Modelica Stefan-Alexander Schneider, Schneider System Consulting16:00-16:05 Closing

13

Appendix B PARTICIPANTSChristian Andersson Joel Andersson Bernhard Bachmann Albert Benveniste Karl BerntorpEnrico Bini Torsten Blochwitz Anders Blomdell Francesco Casella Fernando DAmato Moritz DiehlAdam Duracz Jonas Eborn Johans Eker Hilding Elmqvist Sebastian Engell Alberto Ferrari Niklas ForsPeter Fritzson Claus Fhrer Mahdi Ghazaei Joris Gillis Christian Grussler Manuel Grber Meng Guo Magnus Gfvert Gabriel Hackebeil Mathias HaagePer Hagander Ulf Hagberg Klaus Havelund Grel Hedin Clas Jacobson Jrn JanneckKrzysztof KuchcinskiCarl LairdEdward LeeFredrik Magnusson Sven Erik Mattsson Pieter Mosterman

Lund University KU Leuven Bielefeld University IRISA/INRIALund University Lund University ITI GmbhLund UniversityPolitecnico di MilanoGeneral Electric Global ResearchKU Leuven Halmstad University ModelonEricssonDassault Systmes AB University of Dortmund ALESLund University Linkping University Lund UniversityLund University KU Leuven Lund UniversityTU BraunschweigKTH ModelonTexas A&M UniversityLund University Lund University ABBJPL-NASALund UniversityUnited Technologies Res. CenterLund UniversityLund UniversityTexas A&M University University of California Lund University Dassault Systmes ABMcGill University/Mathworks

chria@maths.lth.se joel.andersson@esat.kuleuven.be bernhard.bachmann@fh-bielefeld.de albert.benveniste@inria.fr karl.berntorp@control.lth.se enrico.bini@control.lth.se Blochwitz@itisim.com anders.blomdell@control.lth.se casella@elet.polimi.it damato@ge.com Moritz.Diehl@esat.kuleuven.be adam.duracz@hh.se jonas.eborn@modelon.com johan.eker@ericsson.com Hilding.ELMQVIST@3ds.com sebastian.engell@bci.tu-dortmund.de alberto.ferrari@ales.eu.com niklas.fors@cs.lth.se peter.fritzson@liu.se claus@maths.lth.se mahdi.ghazaei@control.lth.se joris.gillis@mech.kuleuven.be christian.grussler@control.lth.se m.graeber@tu-bs.demengg@kth.se magnus.gafvert@modelon.com gabehack@gmail.com Mathias.Haage@cs.lth.se per.hagander@control.lth.se ulf.hagberg@se.abb.com klaus@havelund.com Gorel.Hedin@cs.lth.se JacobsCA@utrc.utc.com jwj@cs.lth.se Krzysztof.Kuchcinski@cs.lth.se carl.laird@tamu.edu eal@eecs.berkeley.edu fredrik.magnusson@control.lth.se SvenErik.Mattsson@3ds.com pieter.mosterman@mathworks.com

14 PARTICIPANTS

Anders Nilsson Bjrn Olofsson Hans OlssonAlessandro PapadopoulosAnders RantzerStefan-Alexander SchneiderEelco Scholte Johan Sjberg Emma Sderberg Walid TahaHubertus TummescheitAndreas Varchmin Eric van Wyk Andrea Walther Mike Whalen Daniel WordJohan kesson Karl-Erik rzn Karl Johan strm

Lund University Lund UniversityDassault Systmes AB Politecnico di Milano Lund UniversityBMWUnited Technologies Res. CenterABB Corporate Research Lund University Halmstad University Modelon ABTU Braunschweig University of Minnesota Universitt Paderborn University of Minnesota Texas A&M University Lund University/Modelon Lund UniversityLund University

anders.nilsson@control.lth.se bjorn.olofsson@control.lth.se hans.olsson@3ds.com papadopoulos@elet.polimi.itanders.rantzer@control.lth.seStefan-Alexander.schneider@bmw.de eelco.scholte@utas.utc.com johan.sjoberg@se.abb.com emma.soderberg@cs.lth.se Walid.Taha@hh.se Hubertus.Tummescheit@modelon.com a.varchmin@tu-bs.deevw@cs.umn.edu andrea.walther@uni-paderborn.de whalen@cs.umn.edu dword@tamu.edu johan.akesson@control.lth.se karlerik@control.lth.se karl_johan.astrom@control.lth.se

15

Appendix C PRESENTATIONSNON-STANDARD SEMANTICS OF HYBRID SYSTEMS MODELERSAlbert Benveniste, IRISA/INRIA

Hybrid system modelers have become a corner stone of complex embedded system development. Embedded systems include not only control components and software, but also physical devices. In this area, Simulink is a de facto standard design framework, and Modelica a new player. However, such tools raise several issues related to the lack of reproducibility of simulations (sensitivity to simulation parameters and to the choice of a simulation engine). In this paper we propose using techniques from non-standard analysis to define a semantic domain for hybrid systems. Non-standard analysis is an extension of classical analysis in which in-finitesimal (the and in the celebrated generic sentence of college maths) can be manipulated as first class citizens. This approach allows us to define both a denotational semantics, a constructive semantics, and a Kahn Process Network semantics for hybrid systems, thus establishing simulation engines on a sound but flexible mathematical foundation. These semantics offer a clear distinction between the concerns of the numerical analyst (solving differential equations) and those of the computer scientist (generating execution schemes). We also discuss a num-ber of practical and fundamental issues in hybrid system modelers that give rise to non-reproducibility of results, non-determinism, and undesirable side effects. Of particular importance are casca-ded mode changes (also called zero-crossings in the context of hybrid systems modelers).

16 PRESENTATIONS

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usor

Dis

cret

e?

U

seof

agl

obal

solv

er

no

n-in

tera

ctin

gsu

bsys

tem

sin

tera

ct!

tim

esc

ales

prop

agat

eev

eryw

here

H

ot/C

old

rest

arto

fsol

vers

S

licin

gD

iscr

ete/

Con

tinuo

usis

esse

ntia

l

st

rang

ehy

brid

D+

CS

imul

ink/

Sta

teflo

wdi

agra

ms

can

besp

ecifi

edth

eyge

tstra

nge

retu

rns

from

the

tool

th

eM

odel

ica

cons

ortiu

mha

sm

ade

this

ace

ntra

leffo

rt

Diffi

culti

esin

Hyb

ridS

yste

ms

Mod

eler

s

Som

eex

ampl

es

Non

-Sta

ndar

dH

ybrid

Sys

tem

s(fo

rthe

mat

h-av

erse

)

Non

-Sta

ndar

dA

naly

sis

and

Sta

ndar

disa

tion

(fort

hefa

n)

Non

-Sta

ndar

dH

ybrid

Sys

tem

san

dth

eirS

tand

ardi

satio

n

The

SIM

PLE

HY

BR

IDm

ini-l

angu

age

Con

clus

ion

Som

eex

ampl

es1:

infin

iteca

scad

e

8 < :y

=0

init

1

rese

t[1,

1]ev

ery

up[x

,x]

x=

0in

it

1re

set[

1,1,

1]ev

ery

up[y

,y,

z]z

=1

init

1

Not

eth

atz

isju

sta

phys

ical

cloc

k.S

o,su

chan

exam

ple

can

aris

ew

ithd

iscr

ete

syst

ems

follo

win

gth

edi

scre

te/h

ybrid

clas

sific

atio

nin

forc

ein

the

com

mun

ityof

hybr

idsy

stem

sm

odel

ers.

yx

+1

1

2

34

56

1 here

and

subs

eque

ntly

,is

infin

itesi

mal

Som

eex

ampl

es2:

slid

ing

mod

e

x

=0

init

sg

n(y 0

)re

set[

1,1]

ever

yup

[y,

y]y

=x

init

y 0

23

45

6

+

1

+1

|y

0|

x y

This

isa

sim

ple

form

fora

nA

BS

syst

em.

Cor

resp

ondi

nga

vera

ged

syst

emis

:

y=

sgn(

y 0),

fort

hein

terv

al[0

,|y 0|)

0fo

r[|y

0|,

),

18 PRESENTATIONS

Som

eex

ampl

es3:

finite

casc

ade

8 < :x

=0

init

0re

set[

last

(x)+

1,la

st(x

)+

2]ev

ery

up[y

,z]

z=

1in

it

1y

=0

init

1re

set[

1]ev

ery

up[z

]

1

+1

+2

+3

x y

23

45

61

Her

eth

equ

estio

nis

:ho

wsh

ould

the

rese

ton

xan

dy

bepe

rform

ed?

Her

ew

eha

vead

opte

da

mirc

o-st

epin

terp

reta

tion

refle

ctin

gca

usal

itybe

twee

nth

etw

ore

sets

.A

diffe

rent

inte

rpre

tatio

nis

ofte

npr

opos

edby

exis

ting

mod

eler

s.

Som

eex

ampl

es4:

balls

onw

all

12

w1

d 1

8 > > < > > :

x 1=

v 1in

itd 1

x 2=

v 2in

itd 2

v 1=

0in

itw

1re

setl

ast(

v 2)

ever

yup

[x1

x 2]

v 2=

0in

itw

2re

set[

last

(v1),

last

(v2)]

ever

yup

[x1

x 2,x

2]

Her

eth

edi

fficu

ltyis

the

casc

ade

invo

lvin

g

1.ba

ll1

hitti

ngba

ll2,

resu

lting

inba

ll2

mov

ing

toth

erig

ht(r

eset

)

2.w

hich

caus

esba

ll2

tohi

tthe

wal

lim

med

iate

ly(O

DE

activ

ated

forz

ero

time)

3.re

sulti

ngin

ball

2m

ovin

gba

ckw

ard

(res

et)

4.fo

llow

edby

the

sym

met

ricsh

eme.

Que

stio

ns

C

anw

epr

opos

ea

sem

antic

dom

ain

fort

hese

(and

all)

exam

ples

?

C

anw

eus

eit

to

iden

tify

exam

ple

(1)a

spa

thol

ogic

al,b

utno

texa

mpl

e(2

)?

tode

cide

onth

ese

man

tics

ofex

ampl

e(3

)?

togi

vea

sem

antic

sto

exam

ple

(4)?

M

ore

gene

rally

,can

we

deve

lop

ase

man

ticdo

mai

nto

serv

eas

am

athe

mat

ical

basi

sfo

rthe

man

agem

ento

f(po

ssib

lyca

scad

ed)

zero

-cro

ssin

gs?

yx

+1

1

2

34

56

1

1

+1

+2

+3

x y

23

45

61

12

w1

d 1

(1)

(2)

(3)

(4)

23

45

6

+

1

+1

|y

0|

x y

The

grea

tide

a:no

n-st

anda

rdan

alys

is

Sup

pose

fora

whi

leth

atw

eca

ngi

vea

form

alm

eani

ngto

the

follo

win

g:

y=

xm

eans

,by

defin

ition

:y t

+

y t

=x t

whe

re

isin

finite

sim

al

Lets

mak

ea

tria

luse

ofno

n-st

anda

rdan

aysi

s.Th

e

ofou

rexa

mpl

esw

illbe

iden

tified

with

the

abov

e

.B

ydo

ing

so,o

urdr

awin

gsbe

com

eth

ese

man

tics

ofca

scad

esan

dO

DE

sse

man

tics

isw

ritte

nas

trans

ition

rela

tions

invo

lvin

g

.

19PRESENTATIONS

Diffi

culti

esin

Hyb

ridS

yste

ms

Mod

eler

s

Som

eex

ampl

es

Non

-Sta

ndar

dH

ybrid

Sys

tem

s(fo

rthe

mat

h-av

erse

)

Non

-Sta

ndar

dA

naly

sis

and

Sta

ndar

disa

tion

(fort

hefa

n)

Non

-Sta

ndar

dH

ybrid

Sys

tem

san

dth

eirS

tand

ardi

satio

n

The

SIM

PLE

HY

BR

IDm

ini-l

angu

age

Con

clus

ion

Non

-Sta

ndar

dTi

me

Bas

e

Fix

anin

finite

sim

alba

sest

ep

time

base

:T

={t

n=

n|n

Z}

defin

et

T

: t

=

max

{s|s

T,

st}

Tof

fers

the

butte

rand

the

mon

eyof

the

butte

r(p

opul

arfre

nch

idio

m):

(i)T

isto

tally

orde

red

(ii)

ever

ysu

bset

ofT

that

isbo

unde

dfro

mab

ove

bya

finite

(non

-sta

ndar

d)nu

mbe

rhas

aun

ique

max

imal

elem

ent

(iii)

Tis

dens

ein

RB

y(i)

and

(ii)T

look

sd

iscr

ete

By

(iii),

Tlo

oks

con

tinuo

us

Non

-Sta

ndar

dTi

me

Bas

e

T=

{tn

=n

|n

Z}

t

T:

t

=m

ax{s

|s

T,s

t}

OD

E:

x=

f(x,

u)|

{z}

(pos

sibl

yno

twel

ldefi

ned)

x t=

xt+

f(x

t,u

t)|

{z}

(alw

ays

wel

ldefi

ned)

Stre

ams

ofev

ents

gene

rate

dby

the

zero

-cro

ssin

gsof

x:

x=

def

{t

T|x

t

1 n

ff>

1 n2

ff>

0

clos

eto

+

:

n

y n},

{n|x

n

y n},

{n|x

n

y n},

{n|x

n0

such

that

y

0du

ratio

nw

ithin

mod

es:

OD

E

fin

iteca

scad

esof

mod

ech

ange

s:su

per-

dens

etim

e(t

,n)

R

N

Non

-sta

ndar

d(

-dep

ende

nt)s

eman

tics:

sp

endi

ng

0du

ratio

nw

ithin

mod

es:

non-

stan

dard

OD

E

ca

scad

esof

mod

ech

ange

s:d

iscr

ete

dyna

mic

sin

dexe

dby

T

Theo

rem

:[s

tand

ardi

satio

n]if

the

Sse

man

tics

isw

ell-d

efine

d,th

enit

isth

est

anda

rdis

atio

nof

the

NS

(-d

epen

dent

)sem

antic

s,fo

rany

choi

ceof

27PRESENTATIONS

Non

-Sta

ndar

dH

ybri

dS

yste

ms,

Sta

ndar

disa

tion

Pri

ncip

le

a inv

aria

nt:

dyna

mic

s:V b

gb a(x

)

0x

=f a

(x,t

)

bgb a

(x)

>0

/x

:=zb a

(x,t

)

Sta

ndar

dse

man

tics:

sp

endi

ngst

anda

rd>

0du

ratio

nw

ithin

mod

es:

OD

E

fin

iteca

scad

esof

mod

ech

ange

s:su

per-

dens

etim

e(t

,n)

R

NN

on-s

tand

ard

(-d

epen

dent

)sem

antic

s:

sp

endi

ng

0du

ratio

nw

ithin

mod

es:

non-

stan

dard

OD

E

ca

scad

esof

mod

ech

ange

s:d

iscr

ete

dyna

mic

sin

dexe

dby

T

Theo

rem

:[s

tand

ardi

satio

n]if

the

Sse

man

tics

isw

ell-d

efine

d,th

enit

isth

est

anda

rdis

atio

nof

the

NS

(-d

epen

dent

)sem

antic

s,fo

rany

choi

ceof

Non

-Sta

ndar

dH

ybri

dS

yste

ms,

Sta

ndar

disa

tion

Pri

ncip

le

a inv

aria

nt:

dyna

mic

s:V b

gb a(x

)

0x

=f a

(x,t

)

bgb a

(x)

>0

/x

:=zb a

(x,t

)

Sta

ndar

dse

man

tics:

sp

endi

ngst

anda

rd>

0du

ratio

nw

ithin

mod

es:

OD

E

fin

iteca

scad

esof

mod

ech

ange

s:su

per-

dens

etim

e(t

,n)

R

NN

on-s

tand

ard

(-d

epen

dent

)sem

antic

s:

sp

endi

ng

0du

ratio

nw

ithin

mod

es:

non-

stan

dard

OD

E

ca

scad

esof

mod

ech

ange

s:d

iscr

ete

dyna

mic

sin

dexe

dby

T

Theo

rem

:[s

tand

ardi

satio

n]if

the

Sse

man

tics

isw

ell-d

efine

d,th

enit

isth

est

anda

rdis

atio

nof

the

NS

(-d

epen

dent

)sem

antic

s,fo

rany

choi

ceof

Non

-Sta

ndar

dH

ybri

dS

yste

ms,

Sta

ndar

disa

tion

Pri

ncip

le(e

xten

ded)

11

1

1.2.

3.4.

6.5.

12

21

2w

1

d 1

1w

12

12

22

12

Inth

isex

ampl

e,w

esu

cces

sive

lyha

ve,w

ithin

anin

finite

sim

alpe

riod

oftim

e:

1.a

first

casc

ade

ofz-

c(a

hitc

ausi

ngch

ange

sin

velo

citie

s)

2.th

ela

unch

ing

ofan

OD

Ew

ithan

imm

edia

tez-

c

3.an

othe

rcas

cade

ofz-

c,fo

llow

edby

the

sym

met

ricsc

hem

e.

Pro

vide

dth

atsu

cha

casc

ade

of{z

-c+

OD

Em

icro

-ste

ps}

rem

ains

finite

,a

supe

r-de

nse

time

sem

antic

sca

nbe

give

n.E

xecu

tion

isby

exec

utin

gth

esy

mbo

licno

n-st

anda

rdse

man

tics:

Ext

ende

dS

tand

ardi

satio

nP

rinci

ple.

Non

-Sta

ndar

dH

ybri

dS

yste

ms,

Sta

ndar

disa

tion

Pri

ncip

le(e

xten

ded)

11

1

1.2.

3.4.

6.5.

12

21

2w

1

d 1

1w

12

12

22

12

Non

-sta

ndar

dsy

mbo

licsi

mul

atio

nof

the

colli

ding

balls

exam

ple:

1.t=

,x

1=

w

1>

0

z-c

(zer

o-cr

ossi

ng)o

nx 1

x 2

.

2.

att=

2ba

llsex

chan

geve

loci

ties:

v 1=

0an

dv 2

=w

1.

3.t=

3,x

1=

2w

1an

dx 2

=w

1

OD

Eha

sim

med

iate

z-c

onx 2

4.t=

4,x

1=

x 2=

2w

1,v

1=

0an

dv 2

=

w1.

5.t=

5,x

1=

2w

1an

dx 2

=w

1

z-c

x 1

x 2

6.

att=

6,x

1=

2w

1,x

2=

0,v 1

=

w1

and

v 2=

0.

28 PRESENTATIONS

Diffi

culti

esin

Hyb

ridS

yste

ms

Mod

eler

s

Som

eex

ampl

es

Non

-Sta

ndar

dH

ybrid

Sys

tem

s(fo

rthe

mat

h-av

erse

)

Non

-Sta

ndar

dA

naly

sis

and

Sta

ndar

disa

tion

(fort

hefa

n)

Non

-Sta

ndar

dH

ybrid

Sys

tem

san

dth

eirS

tand

ardi

satio

n

The

SIM

PLE

HY

BR

IDm

ini-l

angu

age

Con

clus

ion

The

SIM

PLE

HY

BR

IDm

ini-l

angu

age

and

itsse

man

tics

T=

def

{n} n

N

xt

=de

fx

t

(n

)=

(n

1)

(n

)=

(n+

1)

stat

emen

ttr

ansi

tion

rela

tion

y=

f(x)

y=

f(x)

y=

last

(x)

init

y 0y

= x

init

y 0

=

up(x

)

=

([ x

0])

y=

xin

ity 0

rese

tz

on\

z:

y=

y+

xon

z:

y=

z

y=

xev

ery

in

ity 0

befo

re

:y

=y 0

on

:y

=x

y=

pre(x

)in

ity 0

y=

xbe

fore

min

(y):

y=

y 0on

y:

y=

x

S1

S2

conj

unct

ion

abor

ting

OD

E

ZC

thre

ety

pes

ofze

ro-c

ross

ing

none

edfo

rle

ft/rig

htlim

it

allZ

C+

abor

ting

OD

Ein

S:

S

The

SIM

PLE

HY

BR

IDm

ini-l

angu

age

and

itsse

man

tics

T=

def

{n} n

N

xt

=de

fx

t

(n

)=

(n

1)

(n

)=

(n+

1)

stat

emen

ttr

ansi

tion

rela

tion

y=

f(x)

y=

f(x)

y=

last

(x)

init

y 0y

= x

init

y 0

=

up(x

)

=

([ x

0])

y=

xin

ity 0

rese

tz

on\

z:

y=

y+

xon

z:

y=

z

y=

xev

ery

in

ity 0

befo

re

:y

=y 0

on

:y

=x

y=

pre(x

)in

ity 0

y=

xbe

fore

min

(y):

y=

y 0on

y:

y=

x

S1

S2

conj

unct

ion

abor

ting

OD

E

ZC

thre

ety

pes

ofze

ro-c

ross

ing

none

edfo

rle

ft/rig

htlim

it

allZ

C+

abor

ting

OD

Ein

S:

S

Slic

ing

disc

rete

com

pile

r

SS

uu

OD

Eso

lver

29PRESENTATIONS

Slic

ing

disc

rete

com

pile

r

SS

uu

OD

Eso

lver

stat

emen

tofS

Ass

igne

dto

SA

ssig

ned

toS

y=

f([x

])on

S

:y

=f(

[x])

outs

ide

S

:y

=f(

[x])

y=

last

(x)

on

S:

y=

last

(x)

outs

ide

S

:y

=la

st(x

)

=

up(x

)

=up

(x)

y=

xin

ity 0

y=

xre

set

zon

S\

S:

y=

xin

ity 0

on

S\

S:

y=

xre

set

zou

tsid

e

S:

y=

xin

ity 0

outs

ide

S

:y

=x

rese

tz

y=

[x]

ever

y[

]y

=[x

]in

ity 0

y=

[x]

ever

y[

]y

=[x

]in

ity 0

y=

pre

(x)

y=

init

y 0y

=pr

e(x

)y

=in

ity 0

Furt

her

use

ofN

on-S

tand

ard

Sem

antic

s

C

ausa

lity

Ana

lysi

san

dC

onst

ruct

ive

Sem

antic

s

co

mpi

latio

nan

dco

dege

nera

tion

cl

ock-

awar

eco

mpi

latio

n

new

appl

icat

ion:

DA

Ean

din

dex

anal

ysis

K

ahn

Net

wor

kse

man

tics

(KP

Nar

gum

ents

exte

ndto

N

)

di

strib

uted

sim

ulat

ion

&m

ultip

leso

lver

sto

avoi

dun

wan

ted

coup

ling

due

toad

aptiv

est

epsi

ze

Diffi

culti

esin

Hyb

ridS

yste

ms

Mod

eler

s

Som

eex

ampl

es

Non

-Sta

ndar

dH

ybrid

Sys

tem

s(fo

rthe

mat

h-av

erse

)

Non

-Sta

ndar

dA

naly

sis

and

Sta

ndar

disa

tion

(fort

hefa

n)

Non

-Sta

ndar

dH

ybrid

Sys

tem

san

dth

eirS

tand

ardi

satio

n

The

SIM

PLE

HY

BR

IDm

ini-l

angu

age

Con

clus

ion

Con

clus

ion

Non

-sta

ndar

dse

man

tics

isno

tjus

tfor

the

fun

ofA

lber

tBen

veni

ste

it

give

sa

sem

antic

sto

alls

ynta

ctic

ally

wel

l-for

med

prog

ram

s

no

hand

wav

ing,

none

edfo

robs

cure

cont

inui

ty/z

eno

assu

mpt

ion

co

mpo

sitio

nal

this

isw

hatt

hela

ngua

gede

sign

erne

eds

pr

ovid

esse

man

ticsu

ppor

tfor

cloc

k-aw

are

caus

ality

anal

ysis

cl

ock-

awar

eco

-sim

ulat

ion

(get

ting

ridof

glob

also

lver

s)

futu

re:

exte

ndto

DA

E

pr

ovid

esse

man

ticsu

ppor

tfor

Dis

cret

e/C

ontin

uous

slic

ing

N

Ssy

mbo

licsi

mul

atio

nof

abor

ting

OD

Es

fu

ture

:si

ngul

arpe

rtur

batio

nsan

dm

ultip

letim

e-sc

ales

Pre

vent

sth

ede

sign

erfro

mth

ene

edfo

rman

uals

moo

thin

g(n

onco

mpo

sitio

nalb

ecau

seba

ndw

idth

-dep

ende

nt)

You

hybr

idgu

ys,g

ole

arni

ngit!

30 PRESENTATIONS

EQUATIONS, SYNCHRONY, TIME, AND MODESEdward A. Lee, EECS, UC Berkeley

The key principle behind equation-based languages is that com-ponents in a system interact with one another not by reacting to inputs to produce outputs, but rather by asserting relationships between the values of variables that they share. This principle is closely related to key principle behind synchronous-reactive (SR) languages, where the meaning of a composition of components is a fixed-point solution to a system of equations. In both cases, interactions between components is a dialog, with give and take, rather than a monolog. SR languages have been used to model discrete behaviors primarily, whereas equation-based languages, particularly Modelica, have been used to model continuous dy-namics primarily. In this talk, I will show how to bridge the two.

Synchronous programs execute a sequence of (conceptually) simultaneous and instantaneous computations. Each step in the sequence is called a tick of a conceptual clock that governs the execution. Distinctly lacking, however, is any notion of metric or measurable time in this clock, so there is no foundation in these languages for modeling continuous dynamics. The ticks form a sequence, not a time line. In fact, a correct execution of a synchronous program (conformant with the semantics) can take as much time as it likes between ticks. The intervals need not even be constant or defined.

In this talk, I will review the principles of synchronous semantics and show how they can be extended to provide a rigorous foun-dation for timed systems that do have a metric notion of time. In particular, I will show how discrete-event (DE) and continuous-time models can be built on top of synchronous semantics. I will also introduce a hierarchical multiform time that allows time progress at different rates in different parts of the system, and I will show how the underlying synchronous semantics ensures determinacy and preserves causality. This multiform model of time provides a foundation for modal behaviors and hybrid systems.

31PRESENTATIONS

Equa

tions

, Sy

nchr

ony,

Ti

me,

and

M

odes

E

dwar

d A

. Lee

R

ober

t S. P

eppe

r Dis

tingu

ishe

d P

rofe

ssor

U

C B

erke

ley

Invi

ted

Talk

at W

orks

hop:

Sy

stem

Des

ign

mee

ts E

quat

ion-

base

d La

ngua

ges:

Wor

ksho

p Pr

ogra

m

Lund

s, S

wed

en,

Sep

t. 18

-21

Col

labo

rativ

e w

ith:

A

dam

Cat

aldo

Patr

icia

Der

ler

Jo

hn E

idso

n

Xiao

jun

Liu

El

efth

erio

s M

atsi

koud

is

H

aiya

ng Z

heng

Lee,

Ber

kele

y 2

Wha

t is

the

mom

entu

m o

f the

mid

dle

ball

as a

func

tion

of ti

me?

p(t)=

mv(

t)

Lee,

Ber

kele

y 3

Wha

t is

the

mom

entu

m o

f the

mid

dle

ball

as a

func

tion

of ti

me?

It

mig

ht s

eem

: p(

t)=

mv(

t)

v(t)=

0

p(t)=

0Le

e, B

erke

ley

4

But

no,

it is

: w

here

t i is

the

time

of c

ollis

ion

v(t)=

{K,

t=t i

0ot

herw

ise

32 PRESENTATIONS

Lee,

Ber

kele

y 5

Sin

ce p

ositi

on is

the

inte

gral

of

vel

ocity

, and

the

inte

gral

of

v is

zer

o, th

e ba

ll do

es n

ot

mov

e.

v(t)=

{K,

t=t i

0ot

herw

ise

K

t i Le

e, B

erke

ley

6

v(t)=

{K,

t=t i

0ot

herw

ise

A d

iscr

ete

repr

esen

tatio

n of

th

is s

igna

l with

sam

ples

is

inad

equa

te.

K

t i

Lee,

Ber

kele

y 7

Sam

ples

yie

ld d

iscr

ete

sign

als

A si

gnal

is

sam

pled

at t

ags

t t 0

t 1 t 2 t

3 t s

...

A s

igna

l s is

dis

cret

e if

ther

e is

an

orde

r em

bedd

ing

from

its

tag

set

( s )

(th

e ta

gs fo

r whi

ch it

is d

efin

ed a

nd n

ot

abse

nt) t

o th

e na

tura

l num

bers

(und

er th

eir u

sual

ord

er).

Not

e: B

enve

nist

e et

al.

use

a di

ffere

nt (a

nd le

ss u

sefu

l?) n

otio

n of

dis

cret

e.

(s)={t0,t 1,...}T

s:TD

Lee,

Ber

kele

y 8

v(t)=

{K,

t=t i

0ot

herw

ise

No

disc

rete

sub

set o

f rea

l-va

lued

tim

es is

ade

quat

e to

un

ambi

guou

sly

repr

esen

t thi

s si

gnal

. K

t i

33PRESENTATIONS

Lee,

Ber

kele

y 9

v(t)=

{K,

t=t i

0ot

herw

ise

Ther

e is

no

sem

antic

di

stin

ctio

n be

twee

n a

disc

rete

even

t and

a ra

pidl

y va

ryin

g co

ntin

uous

sig

nal.

K

t i Le

e, B

erke

ley

10

Sim

ulin

k/S

tate

flow

can

not a

ccur

atel

y m

odel

suc

h ev

ents

.

In S

imul

ink,

a s

igna

l can

onl

y ha

ve o

ne v

alue

at a

giv

en ti

me.

Hen

ce

Sim

ulin

k in

trodu

ces

solv

er-d

epen

dent

beh

avio

r.

Lee,

Ber

kele

y 1

1

1

1

Pto

lem

y II

uses

Sup

erde

nse

Tim

e [M

aler

, Man

na, P

nuel

li, 9

2]

for C

ontin

uous

-Tim

e S

igna

ls

At e

ach tag,

the

sign

al h

as e

xact

ly o

ne v

alue

. At e

ach

time

poin

t, th

e si

gnal

has

a s

eque

nce

of v

alue

s. S

igna

ls a

re p

iece

wis

e co

ntin

uous

, in

a w

ell-d

efin

ed te

chni

cal s

ense

, a p

rope

rty th

at m

akes

OD

E s

olve

rs w

ork

wel

l.

v:(R

N)

R3

v(t i,

0)=

0In

itial

val

ue:

Inte

rmed

iate

val

ue:

Fina

l val

ue:

v(t i,

1)=

K

v(t i,

n)=

0,n

2

Lee,

Ber

kele

y 1

2

Con

sequ

ence

s of

usi

ng S

uper

dens

e Ti

me

Tra

nsie

nt s

tate

s ar

e w

ell r

epre

sent

ed:

Inf

inite

ssim

als

(eve

n D

irac

delta

func

tions

):

Lee

LLLee

Lee

Lee,

LLLLLLLLLLLLLLLLLLLLLLLLLLLeB

erBBB

erB

erB

erBBBBBBBBBBBBBBBBBBBBBBBB

keleelkeleekele

keleeeeeeekeeeeeeeeekeeeeeekeeeeeee

y11

y1

y 1

y 111 11111 11111

2222

34 PRESENTATIONS

Lee,

Ber

kele

y 1

3

Mor

e C

onse

quen

ces:

H

ybrid

Sys

tem

Fi

nite

Sta

te M

achi

ne

Dya

nmic

s 1

Dyn

amic

s 2

Lee,

Ber

kele

y 1

4

Tran

sitio

ns b

etw

een

mod

es a

re in

stan

tane

ous

In th

e si

gnal

s at

the

right

, the

vel

ociti

es

and

acce

lera

tions

pro

ceed

thro

ugh

a se

quen

ce o

f val

ues

at th

e tim

es o

f the

co

llisi

ons

and

sepa

ratio

ns.

Lee,

Ber

kele

y 1

5

1

5

Sup

erde

nse

Tim

e

The

red

arro

ws

indi

cate

val

ue c

hang

es b

etw

een

tags

, whi

ch c

orre

spon

d to

dis

cont

inui

ties.

Sig

nals

are

con

tinuo

us fr

om th

e le

ft an

d co

ntin

uous

fro

m th

e rig

ht a

t poi

nts

of d

isco

ntin

uity

.

Lee,

Ber

kele

y 1

6 Le

e, B

erke

ley

16

Mod

al M

odel

s an

d M

ultif

orm

Tim

e O

nce

we

have

a

clea

n, in

stan

tane

ous

hand

off b

etw

een

mod

es, a

que

stio

n ar

ises

abo

ut h

ow to

m

odel

tim

e is

a

dorm

ant m

ode.

Act

or

Ref

inem

ent

FSM

Sta

te

Tran

sitio

n

Ref

inem

ent

Por

ts

Por

ts

Whe

n th

is m

ode

is in

activ

e,

shou

ld ti

me

adva

nce?

35PRESENTATIONS

Lee,

Ber

kele

y 1

7

The

Mod

al M

odel

Mud

dle

Its

abou

t tim

e A

fter t

ryin

g se

vera

l var

iant

s on

the

sem

antic

s of

mod

al

time,

we

settl

ed o

n th

is:

A m

ode

refin

emen

t has

a lo

cal n

otio

n of

tim

e. W

hen

the

mod

e re

finem

ent i

s in

activ

e, lo

cal t

ime

does

not

adv

ance

. Lo

cal t

ime

has

a m

onot

onic

ally

incr

easi

ng g

ap re

lativ

e to

en

viro

nmen

t tim

e.

Lee,

Ber

kele

y 1

8 1

Mul

tiFor

m T

ime

in P

tole

my

II

susp

end

resu

me

refe

renc

e tim

e

loca

l tim

e In

Pto

lem

y II

Mod

al M

odel

s,

Tim

e is

sus

pend

ed a

nd re

sum

ed

Lee,

Ber

kele

y 1

9

Var

iant

s fo

r the

Sem

antic

s of

Mod

al T

ime

that

we

Trie

d or

Con

side

red,

but

that

Fai

led

Mod

e re

finem

ent e

xecu

tes

whi

le i

nact

ive

but

inpu

ts a

re n

ot

prov

ided

and

out

puts

are

not

obs

erve

d.

Tim

e ad

vanc

es w

hile

mod

e is

inac

tive,

and

mod

e re

finem

ent

is re

spon

sibl

e fo

r ca

tchi

ng u

p.

Mod

e re

finem

ent i

s n

otifi

ed w

hen

it ha

s re

ques

ted

time

incr

emen

ts th

at a

re n

ot m

et b

ecau

se it

is in

activ

e.

Whe

n a

mod

e re

finem

ent i

s re

-act

ivat

ed, i

t res

umes

from

its

first

mis

sed

even

t. A

ll of

thes

e le

d to

som

e ve

ry s

trang

e m

odel

s

Fina

l sol

utio

n: L

ocal

tim

e do

es n

ot a

dvan

ce w

hile

a m

ode

is

inac

tive.

Mon

oton

ical

ly g

row

ing

gap

betw

een

loca

l tim

e an

d en

viro

nmen

t tim

e.

Lee,

Ber

kele

y 2

0

Onc

e w

e ha

ve m

ultif

orm

tim

e, w

e ca

n bu

ild a

ccur

ate

mod

els

of c

yber

-phy

sica

l sys

tem

s

36 PRESENTATIONS

Lee,

Ber

kele

y 2

1

Eng

inee

rs m

odel

phy

sica

l dyn

amic

s us

ing

di

ffere

ntia

l-alg

ebra

ic e

quat

ions

.

The

varia

ble

t re

pres

ents

an

idea

lized

N

ewto

nian

no

tion

of

time.

Le

e, B

erke

ley

22

But

com

puta

tiona

l pla

tform

s ha

ve n

o ac

cess

to t.

In

stea

d, lo

cal m

easu

rem

ents

of t

ime

are

used

.

A su

perd

ense

N

ewto

nian

no

tion

of ti

me

beco

mes

en

viro

nmen

t tim

e

Lee,

Ber

kele

y 2

3

Loca

l tim

e w

ithin

a h

iera

rchy

ca

n ad

vanc

e at

diff

eren

t rat

es.

Mod

el u

ses

ora

cle

time,

w

hich

bec

omes

env

ironm

ent t

ime

fo

r the

sub

syst

ems.

Mod

el in

tern

ally

use

s lo

cal t

ime

Dis

cret

e E

vent

MoC

Mod

el in

tern

ally

use

s lo

cal t

ime

Lee,

Ber

kele

y 2

4

Clo

cks

drift

Fab

ricat

ion

tole

ranc

e A

ging

T

empe

ratu

re

Hum

idity

V

ibra

tions

Q

ualit

y of

the

quar

tz.

Clo

ck d

rifts

mea

sure

d in

pa

rts p

er m

illio

n o

r ppm

1

ppm

cor

resp

onds

to a

dev

iatio

n of

1s

eve

ry s

econ

d

37PRESENTATIONS

Lee,

Ber

kele

y 2

5

Mul

tiFor

m T

ime

in P

tole

my

refe

renc

e tim

e

loca

l tim

e

Hea

ven

for e

ngin

eers

. Lo

cal t

ime

and

envi

ronm

ent

time

are

in s

ync!

Lee,

Ber

kele

y 2

6 2

Mul

tifor

m T

ime

in th

e R

eal W

orld

offs

et

refe

renc

e tim

e

loca

l tim

e R

ealit

y:

Ther

e is

an

offs

et b

etw

een

loca

l tim

e an

d en

viro

nmen

t tim

e

Lee,

Ber

kele

y 2

7 2

Mul

tifor

m T

ime

in P

tole

my

fast

clo

ck

slow

clo

ck refe

renc

e tim

e

loca

l tim

e M

ore

real

: clo

cks

drift

Lee,

Ber

kele

y 2

8 2

Mul

tifor

m T

ime

in P

tole

my

envi

ronm

ent t

ime:

t e st

art t

ime:

s e

, sl

offs

et:

o =

s e -

s l cl

ock

rate

: c l lo

cal t

ime:

t l =

(te - o

) c

l

t e

t l

s e

s lo

c l =

1.0

c l=

0.5

se

t clo

ck d

rift

Eve

n m

ore

real

: clo

ck d

rift c

hang

es!

38 PRESENTATIONS

Lee,

Ber

kele

y 2

9 2

Mul

tifor

m T

ime

in P

tole

my

envi

ronm

ent t

ime:

t e st

art t

ime:

s e

, sl

offs

et:

o =

s e -

s l cl

ock

rate

: c l lo

cal t

ime:

t l =

(te - o

) c

l

t e

t l

s e

s lo

c l =

1.0

c l=

0.5

se

t clo

ck d

rift

Pto

lem

y II

prov

ides

a

hier

arch

y of

loca

l clo

cks

This

can

be

used

, for

exa

mpl

e, to

acc

urat

ely

mod

el ti

me

sync

hron

izat

ion

prot

ocol

s.

Lee,

Ber

kele

y 3

0

Mul

tifor

m T

ime

is In

trins

ic!

Tim

e

Phys

ical

M

easu

red

Rela

tivis

tic

New

toni

an

Mic

ropr

oces

sor

Clo

ck

Sync

hron

ized

C

lock

NTP

PT

P, IE

EE 1

588

GPS

Mas

ter C

lock

TA

I

Tim

e in

physical

law

s,

mat

hem

atic

al,

cont

inuo

us

Tim

e in

digital s

yste

ms

Circ

uits

, dis

cret

e cl

ocks

, ge

nera

ting

wel

l def

ined

pe

riodi

c si

gnal

s

Clo

ck

sync

hron

izat

ion

Sou

rce:

Pat

ricia

Der

ler a

nd J

ohn

Eid

son

Lee,

Ber

kele

y 3

2

Oth

er Q

uest

ions

abo

ut T

ime:

1.

Pre

cisi

on

In fl

oatin

g-po

int f

orm

ats,

pr

ecis

ion

degr

ades

as

mag

nitu

de in

crea

ses

2.

Cle

ar S

eman

tics

of S

imul

tane

ity

Req

uire

s pr

ecis

e ad

ditio

n an

d su

btra

ctio

n, e

.g.

(a

+ b

) + c

= a

+ (b

+ c

). Fl

oatin

g-po

int n

umbe

rs d

ont

have

this

pro

perty

. Fl

oatin

g po

int n

umbe

rs a

re a

poo

r cho

ice

for m

odel

ing

time!

Lee,

Ber

kele

y 3

3

Con

clus

ions

Mod

elin

g tim

e as

a s

impl

e co

ntin

uum

is n

ot a

dequ

ate.

S

uper

dens

e tim

e of

fers

cle

an s

eman

tics

for i

nsta

ntan

eous

ev

ents

.

Hom

ogen

eous

tim

e ad

vanc

ing

unifo

rmly

is n

ot a

dequ

ate.

H

iera

rchi

cal m

ultif

orm

tim

e en

able

s ac

cura

te a

nd p

ract

ical

m

odel

s of

het

erog

eneo

us d

istri

bute

d sy

stem

s.

Flo

atin

g po

int n

umbe

rs fo

r tim

e ar

e no

t ade

quat

e.

A m

odel

with

inva

riant

pre

cisi

on a

nd p

reci

se a

dditi

on a

nd

subt

ract

ion

is.

39PRESENTATIONS

FORMAL MODELING AND ANALYSIS OF SOFTWARE SYSTEMS WITH LUSTREMike Whalen, University of Minnesota

Rockwell Collins and the University of Minnesota have used the synchronous dataflow language Lustre as a basis for a variety of analyses of industrial critical systems both for component level models written in Simulink and system architectural models writ-ten in AADL. This talk describes the approach, several examples of analyzed models as well as several challenges to extend the scale and variety of systems that can be practically analyzed.

40 PRESENTATIONS

Softw

are

Engi

neer

ing

Cen

ter

Mik

e W

hale

n Pr

ogra

m D

irect

or

Uni

vers

ity o

f Min

neso

ta S

oftw

are

Engi

neer

ing

Cen

ter

Spon

sore

d by

NSF

Res

earc

h G

rant

C

NS-

1035

715

Roc

kwel

l Col

lins

(Dar

ren

Cof

er, A

ndre

w

Gac

ek, S

teve

n M

iller

, Luc

as W

agne

r)

UPe

nn: (

Insu

p Le

e, O

leg

Soko

lsky

) U

MN

(M

ats

P. E.

Hei

mda

hl)

CM

U S

EI (

Pete

r Fe

iler)

Sept

embe

r, 20

12

2 LC

CC

201

2: M

ike

Wha

len

Sept

embe

r, 20

12

LCC

C 2

012:

Mik

e W

hale

n 3

Febr

uary

, 201

2 IF

IP 2

012:

Mik

e W

hale

n 4

Syst

em d

esig

n &

ver

ifica

tion

thro

ugh

patt

ern

appl

icat

ion

and

com

posi

tiona

l rea

soni

ng

CO

MPU

TIN

G

RES

OU

RC

E SE

NSO

R

LRU

FAIL

-SIL

ENT

N

OD

E FR

OM

R

EPLI

CA

S

CO

MPU

TIN

G

RES

OU

RC

E A

CO

MPU

TIN

G

RES

OU

RC

E B

VOT

E M

ULT

IPLE

D

ATA

SEN

SOR

1

SEN

SOR

2

SEN

SOR

3

VER

IFIE

D AV

AIL

ABI

LIT

Y V

ERIF

IED

INT

EGR

ITY

AR

CH

ITEC

TU

RE

MO

DEL

CO

MPO

SIT

ION

AL

PRO

OF

OF

CO

RR

ECT

NES

S (A

SSU

ME

G

UA

RA

NT

EE)

SAFE

TY,

BEH

AVIO

RA

L,

PER

FOR

MA

NC

E PR

OPE

RTIE

S

ABSTRACTION VERIFICATION

REUSE

CO

MP

OSI

TIO

N

C

opyr

ight

201

1 Roc

kwel

l Col

lins,

Inc

.

All

righ

ts r

eser

ved.

41PRESENTATIONS

Sept

embe

r, 20

12

LCC

C 2

012:

Mik

e W

hale

n 5

PATT

ERN

&

CO

MP

SPE

C

LIBRARY

SYS

TEM

M

OD

ELIN

G

ENVIR

ON

MEN

T

INSTA

NTI

ATE

ARCH

ITEC

TURAL

PATT

ERN

S

SYS

TEM

M

OD

EL

AU

TO

GEN

ERAT

E

SYS

TEM

IM

PLEM

ENTA

TIO

N

ARCH

PA

TTER

N

MO

DEL

S

CO

MPO

NEN

T M

OD

ELS

AN

NO

TATE

&

VER

IFY

MO

DEL

S

CO

MPO

NEN

T LI

BRARY

SPE

CIF

ICAT

ION

SYS

TEM

DEV

ELO

PMEN

T FO

UN

DRY

CO

MPO

SIT

ION

AL

REA

SO

NIN

G &

AN

ALY

SIS

OD

ELIN

G

IRO

NM

ENENEEEENEEEEENENENNEENEENEENNENNNEENNT

MO

DEL

CO

MPO

SIT

ION

AL

REA

SO

NIN

G &

AN

ALY

SIS

Inst

an

tiati

on

: Che

ck s

truc

tura

l con

stra

ints

, Em

bed

assu

mpt

ions

&

guar

ante

es in

sys

tem

mod

el

L LALL

ALLLLLLLLL

&

Co

mp

osi

tio

nal V

eri

fica

tio

n:

Sys

tem

pro

pert

ies

are

verifie

d by

mod

el c

heck

ing

usin

g co

mpo

nent

& p

atte

rn

cont

ract

s

LIBRARY

CCO

MPPPPPPPPPPPPPPPPPPPPPPPPPP

CCO

MPPPPPPPPPPP

ENT TTTTT

NTTT

PPPPOOPPPPPOOPPOOOON

OONN

MMOOOOOOOOOOOOOOOOOO

DO

DMM

OOOOOOOOOOOOOODD

LLSS

DDE

DDEELLELL

CO

MPO

NEN

T LI

BRARY

Reu

sab

le V

eri

fica

tio

n:

Proo

f of

com

pone

nt a

nd p

atte

rn

requ

irem

ents

(gu

aran

tees

) an

d sp

ecifi

cation

of

cont

ext

(ass

umpt

ions

)

C

opyr

ight

201

1 Roc

kwel

l Col

lins,

Inc

.

All

righ

ts r

eser

ved.

Avi

onic

s sy

stem

req

requ

irem

ent

Rel

ies

upon

Acc

urac

y of

air

dat

a se

nsor

s

Con

trol

com

man

ds fr

om F

CS

Mod

e of

FG

S F

GS

cont

rol l

aw b

ehav

ior

Fai

love

r be

havi

or b

etw

een

FGS

syst

ems

.

R

espo

nse

of A

ctua

tors

Tim

ing/

Lag/

Late

ncy

of

Com

mun

icat

ions

Se

ptem

ber,

2012

LC

CC

201

2: M

ike

Wha

len

6

FCS

Avi

onic

s Sy

stem

U

nder

sin

gle-

faul

t as

sum

ptio

n,

GC

out

put

tran

sien

t re

spon

se is

bo

unde

d in

tim

e an

d m

agni

tude

Aut

opilo

t FG

S_L

FGS_

R

AD

S_L

AD

S_R

Syst

em

Mod

es

Con

trol

La

ws

Co-

ord

W

ant

to p

rove

a t

rans

ient

re

spon

se p

rope

rty

T

he a

utop

ilot

will

not

cau

se a

sha

rp

chan

ge in

pitc

h of

airc

raft.

Ev

en w

hen

one

FGS

fails

and

the

ot

her

assu

mes

con

trol

G

iven

ass

umpt

ions

abo

ut t

he

envi

ronm

ent

T

he s

ense

d ai

rcra

ft pi

tch

from

the

ai

r da

ta s

yste

m is

with

in s

ome

abso

lute

bou

nd a

nd d

oesn

t ch

ange

to

o qu

ickl

y

T

he d

iscr

epan

cy in

sen

sed

pitc

h be

twee

n le

ft an

d ri

ght

side

sen

sors

is

boun

ded.

an

d gu

aran

tees

pro

vide

d by

co

mpo

nent

s

Whe

n a

FGS

is a

ctiv

e, it

will

gen

erat

e an

acc

epta

ble

pitc

h ra

te

A

s w

ell a

s fa

cts

prov

ided

by

patt

ern

appl

icat

ion

Le

ader

sel

ectio

n: a

t le

ast

one

FGS

will

alw

ays

be a

ctiv

e (m

odul

o on

e f

ailo

ver

ste

p)

Sept

embe

r, 20

12

LCC

C 2

012:

Mik

e W

hale

n 7

transient_response_1 : assert true ->

abs(CSA.CSA_Pitch_Delta) < CSA_MAX_PITCH_DELTA ;

transient_response_2 : assert true ->

abs(CSA.CSA_Pitch_Delta - prev(CSA.CSA_Pitch_Delta, 0.0))

< CSA_MAX_PITCH_DELTA_STEP ;

A

vion