EECE 396-1 Hybrid and Embedded Systems: Computation

EECE 396-1Hybrid and Embedded Systems: Computation

T. John Koo, Ph.D.Institute for Software Integrated Systems

Department of Electrical Engineering and Computer ScienceVanderbilt University

300 Featheringill HallApril 20 , 2004

[email protected]://www.vuse.vanderbilt.edu/~kootj

2

Summary

3

Hybrid System A system built from atomic discrete

components and continuous components by parallel and serial composition, arbitrarily nested.

The behaviors and interactions of components are governed by models of computation (MOCs).

Discrete Components Finite State Machine (FSM) Discrete Event (DE) Synchronous Data Flow (SDF)

Continuous Components Ordinary Differential Equation (ODE) Partial Differential Equation (PDE)

q1q2 q3

u

xç = f (x) + g(x)u

x

4

Why Hybrid Systems? Modeling abstraction of

Continuous systems with phased operation (e.g. walking robots, mechanical systems with collisions, circuits with diodes)

Continuous systems controlled by discrete inputs (e.g. switches, valves, digital computers)

Coordinating processes (multi-agent systems) Important in applications

Hardware verification/CAD, real time software Manufacturing, communication networks, multimedia

Large scale, multi-agent systems Automated Highway Systems (AHS) Air Traffic Management Systems (ATM) Uninhabited Aerial Vehicles (UAV) Power Networks

5

Topics Modeling

Finite State Machines Time Automata Ordinary Differential Equations Hybrid Automata

Analysis Reachability - Discrete Reachability - Continuous Reachability - Hybrid

Tool Ptolemy II HyTech Requiem d/dt Checkmate

Verification Temporal Logic Model Checking Time Automata

q1q2 q3

u

xç = f (x) + g(x)u

x

6

Hybrid Automaton

7

Hybrid Automaton Hybrid Automaton (Lygeros, 2003)

8

Hybrid Automaton

Q

X

Execution

9

Examples: Thermostat

t

10

Examples: Bouncing Ball

11

Motivating Examples:Two Tanks

12

Hybrid Automaton

t

i

012

34

13

Hybrid Automaton

i

012

34

t

14

Hybrid Automaton

i

012

34

t

15

Hybrid Automaton

16


17

Hybrid Automaton

i

012

tfinite

i

012

tinfinite

18

Hybrid Automaton

i

012

tfinite

i

012

tZeno

19

Hybrid Automaton Zeno of Elea, 490BC

Ancient Greek philosopher The race of Achilles and the turtle

Achilles, a renowned runner, was challenged by the turtle to a race. Being a fair sportsman, Achilles decided to give the turtle a 10 meter head-start. To overtake the turtle, Achilles will have to first cover half the distance separating them. To cover the remaining distance, he will have to cover half that distance, and so on.

No matter how fast Achilles is, he can never overtake the turtle. Why???

Ans: Covering each one of the segments in this series requires a non zero amount of time. Since there is an infinite number of segments, Achilles will never overtake the turtle.

20

Hybrid Automaton Non-Determinism

Multiple Executions for the same initial condition Sources of non-determinism

Non-Lipschitz continuous vectorfields, f Multiple discrete transition destinations, E & G Choice between discrete transition and continuous evolution, D & G Non-unique continuous state assignment, R

Definition: A hybrid automaton H is deterministic if for all initial conditions there exists a unique maximal sequence

21

Hybrid Automaton Blocking

No Infinite executions for some initial states Source of blocking

Cannot continue in domain due to reaching the boundary of the domain where no guard is defined

Have no place to make discrete transition to

Definition: A hybrid automaton H is non-blocking if for every initial condition there exists at least one infinite execution

?

22

Hybrid Automaton Zeno Executions

Infinite execution defined over finite time Infinite number of transitions in finite time Transition times converge

Definition: A hybrid automaton H is zeno if there exists an initial condition for which all infinite executions are Zeno

23

Exercise

24


Is this model: Deterministics? Non-Blocking? Zeno?

25


Is this model: Deterministics?

Yes, the Guard and Domain contains only one element. Reset maps from one point to exactly another point. Also, the vector field is Lipschitz continuous.

Non-Blocking? Zeno?

26


Is this model: Deterministics? Non-Blocking?

Yes, the guard is always reachable from any initial condition within the domain and also the reset makes the state start within the domain.

Zeno?

27


28


29


30



Yes, it is Zeno since the time sequence converges.

31

Thermostat


32

Thermostat

Is this model: Deterministics? No. Non-Blocking? Yes. Zeno? No.

33

Two Tanks

Is this model: Deterministics? Yes. Non-Blocking? Yes. Zeno? Yes.

34

Zeno—infinitely many jumps in finite time

If

Water Tank Automaton

35

Timed Automata


36

Timed Automata

Is this model: Deterministics? No. Non-Blocking? Yes. Zeno? No.

37

In Summary

Deterministic Non-Blocking Zeno

Thermostat NO YES NO

Bouncing Ball YES YES YES

Two Tanks YES YES YES

Time Automaton

NO YES NO

38

In Summary

Deterministic Non-Blocking Zeno

Thermostat NO YES NO

Bouncing Ball YES YES YES

Two Tanks YES YES YES

Time Automaton

NO YES NO

Mapping

Verification

Special Attention in Simulation

Verification

39

Computational Tools

40

Computational Tools Simulation

Ptolemy II: ptolemy.eecs.berkeley.edu Modelica: www.modelica.org SHIFT: www.path.berkeley.edu/shift Dymola: www.dynasim.se OmSim: www.control.lth.se/~cace/omsim.html ABACUSS: yoric.mit.edu/abacuss/abacuss.html Stateflow: www.mathworks.com/products/stateflow CHARON: http://www.cis.upenn.edu/mobies/charon/ Masaccio: http://www-cad.eecs.berkeley.edu/~tah/Publications/masaccio.html

41

Computational Tools Simulation

Models of Computation

System Complexity

Ptolemy II

DymolaModelica

ABACUSS

SHIFT

OmSim

MasaccioCHARON

StateFlow/Simulink

42

Computational Tools Verification

FiniteAutomata

TimedAutomata

LinearAutomata

LinearHybrid Systems

NonlinearHybrid Systems

d/dtCheckMate

Timed COSPANKRONOSTimed HSISVERITIUPPAAL

HYTECHCOSPANSMVVIS…

Requiem

43

End

Documents

EECE 396-1 Hybrid and Embedded Systems: Computation