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 HallJanuary 14, 2004

john.koo@vanderbilt.eduhttp://www.vuse.vanderbilt.edu/~kootj

2

Hybrid SystemsUC Berkeley

Spring 2002 by T. John Koo, S. Shankar Sastryhttp://robotics.eecs.berkeley.edu/~koo/Sp02/Spring 2001 by T. John Koo, S. Shankar Sastryhttp://robotics.eecs.berkeley.edu/~koo/Sp01/Spring 2000 by Karl. H. Johansson, Luca de Alfaro, Thomas A. Henzingerhttp://www.s3.kth.se/~kallej/eecs291e/Spring 1999 by John Lygeros, S. Shankar Sastryhttp://robotics.eecs.berkeley.edu/~lygeros/Teaching/ee291E.htmlSpring 1998 by Thomas A. Henzinger, S. Shankar Sastry

Stanford UniversitySpring 2002 by Claire Tomlinhttp://www.stanford.edu/class/aa278a/

University of PennsylvaniaFall 2000 by Rajeev Alur, George J. Pappashttp://www.seas.upenn.edu/~pappasg/EE601/

3

Hybrid SystemA 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 ComponentsFinite State Machine (FSM)Discrete Event (DE)Synchronous Data Flow (SDF)

Continuous ComponentsOrdinary Differential Equation (ODE)Partial Differential Equation (PDE)

q1q2

q3

u

xç = f(x) + g(x)u

x

4

Hybrid SystemContinuous systems with phased operations

Bouncing ballCircuits with diodesSwitching circuits

Continuous systems controlled by discrete inputs

ThermostatWater tank Engine control systemsMulti-modal systemsEmbedded control systems

q1q2

q3

u

xç = f(x) + g(x)u

x

5

The Heterogeneity of Systems

power train

embedded controller sensors

fuel air

E H

C I

engine

Continuous Time

Finite StateMachine

Discrete Event

An Engine Control System

6

Models of Computation

power train

embedded controller sensors

fuel air

E H

C I

engine

Continuous Time• continuous functions• continuous time• continuous signals

Finite State Machine• states• transitions

Discrete Event• operations on events• continuous time• discrete events

7

The Hierarchical View of Systems

controller

I CH

car model

engine powertrain

E

8

Embedded Systems

Embedded systems composed of hardware and software components are designed to interact with a physical environment in real-time in order to fulfill control objectives and design specifications.

Environment

Embedded Hardware

Board Support Packages

Operating System

Embedded Software

9

Embedded Systems

Embedded software refers to application software to process information to and fro between the informationand physical worlds.

Environment

Embedded Hardware

Board Support Packages

Operating System

Embedded Software

q1q2

q3

u

xç = f(x) + g(x)u

x

D/A A/D

10

High-ConfidenceEmbedded Software

From Design to Implementation

q1q2

q3

u(t)

xç = f(x) + g(x)u

x(t)

GPS Card INSServos

q1q2

q3

x(t)u(t)

x[k]u[k]

How?

1. Guaranteed closed-loop performance

2. Interaction between asynchronous and synchronous components

Embedded Computer

EmbeddedSoftware

11

GroundStation

DQICONT

DQIGPS

INS UpdateINS Update Boeing DQI-NP

100Hz

PRTK@ 5HzPXY@1Hz

Flight Status

Command

NovAtel GPS RT-2

GPS UpdateGPS Update

ULREADUltrasonic Ultrasonic sensors@4sensors@4±1Hz1HzVCOMM

Relative AltitudeControl outputat 50Hz

Nav data

DGPS measurement

Nav Data to Vision computer

@10Hz

RS-232

Shared Memory

Radio link

RX valuesRX values Yamaha Receiver(using HW INT & proxy)

Ground computerWin 98

Processesrunning on QNX

4±1Hz10Hz

ANYTIME

APERIODIC

PERIODIC

PERIODIC

PERIODIC

High-Confidence Embedded Software

12

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 applicationsHardware verification/CAD, real time softwareManufacturing, communication networks, multimedia

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

13

Different Approaches

14

High-Confidence Embedded Systems• Correctness by construction• Fault-tolerance• Resistance to attack

200 Hz 400

Hz

200 Hz

1 kHz

Flight Control Software

Embedded Software• Embedded software refers to application software to process

information to and fro between the information and physical worlds.

Environment

Embedded Hardware

Board Support Packages

Operating System

Embedded Software

Network-Centric Distributed Systems• Cooperative Control of Multiple UAVs• Power Electronics Circuits• Sensor Networks

Hybrid SystemsControl Theory

Control of individual agentsContinuous modelsDifferential equations

Computer ScienceModels of computationCommunication modelsDiscrete event systems

Hybrid Systems

Research Directions

15

What Are Hybrid Systems?

Dynamical systems with interacting continuous and discrete dynamics

16

Proposed Framework

Control TheoryControl of individual agentsContinuous modelsDifferential equations

Computer ScienceModels of computationCommunication modelsDiscrete event systems

Hybrid Systems

17

ENNA GmbH

Power ElectronicsPower electronics found in:

DC-DC converters Power suppliesElectric machine drives

Circuits can be defined as networks of:Voltage and current sources (DC or AC)Linear elements (R, L, C)Semiconductors used as switches (diodes, transistors)

18

ENNA GmbH

Power ElectronicsDiscrete dynamics

N switches, (up to) 2N discrete statesOnly discrete inputs (switching): some discrete transitions under control, others not

Continuous dynamicsLinear or affine dynamics at each discrete state

+ +

23=8 possible configurations

19

Power Electronics : DC-DC Converters

Have a DC supply (e.g. battery), but need a different DC voltageDifferent configurations depending on whether Vin<Vout or Vin>VoutControl switching to maintain Vout with changes in load (R), and Vin

Vin

L C Rsw1

sw2+

-

+

-Vout

iL

iL

Vout

2 1 2

20

Two Output DC-DC Converter

Want two DC output voltagesInductors are big and heavy, so only want to use oneSimilar to “two tank” problem

Vin

L

C2 R2sw1

sw2+

-

+

-VoutA

iL+

-VoutB

sw3C3 R3

iL

VoutA

VoutB

1 2 3 1 2 3

21

Circuit OperationOne and only one switch closed at any timeEach switch state has a continuous dynamics

sw1: iL↑ , VoutA↓ , VoutB↓

sw2: iL ↓ , VoutA ↑ , VoutB↓ sw3: iL ↓ , VoutA↓ , VoutB ↑

22

Design Objective

Objective: Regulate two output voltages and limit current by switching between three discrete states with continuous dynamics.

iL↑ , VoutA↓ , VoutB↓

iL ↓ , VoutA ↑ , VoutB↓

iL ↓ , VoutA↓ , VoutB ↑

23

Typical Circuit Analysis/Control

Governing equationsTime domain, steady stateEnergy balance

System dynamicsDiscretization in time

Switched quantity only sampled at discrete instantsAssumes a fixed clock

AveragingSwitched quantity approximated by a moving averageAssumes switching is much faster than system time constants

ControlLinearize with duty (∆) as inputUse classical control techniques

T

∆ T (1- ∆)T

i0

i1

i2

match!

iL(t)iL(t)

iL[k]

24

Outline

Background on Power ElectronicsHybrid Modeling of DC-DC ConvertersControlled Invariant BallsConclusions

Vin

L C Rsw1

sw2+

-

+

-Vout

iL

25

Problem Formulation

26

q1

xç (t) = fq1(x(t))x(t) ∈ Iq1

q2

xç (t) = fq2(x(t))x(t) ∈ Iq2

û = û2

û = û1

q1

û = û1

q2

û = û2

x ∈ G12

x ∈ G21

û ∈ Σ

x ∈ X

H1

H2

Problem FormulationParallel Composition of Hybrid Automata

Given a collection of Modes and Edges, design Guards

27

Research Issues Modeling & Simulation

Control: classify discrete phenomena, existence and uniqueness of execution, Zeno [Branicky, Brockett, van der Schaft, Astrom]Computer Science: composition and abstraction operations [Alur-Henzinger, Lynch, Sifakis, Varaiya]

Analysis & VerificationControl: stability, Lyapunov techniques [Branicky, Michel], LMI techniques [Johansson-Rantzer]Computer Science: Algorithmic [Alur-Henzinger, Sifakis, Pappas-Lafferrier-Sastry] or deductive methods [Lynch, Manna, Pnuelli], Abstraction [Pappas-Tabuada, Koo-Sastry]

Controller SynthesisControl: optimal control [Branicky-Mitter, Bensoussan-Menaldi], hierarchical control [Caines, Pappas-Sastry], supervisory control [Lemmon-Antsaklis], safety specifications [Lygeros-Sastry, Tomlin-Lygeros-Sastry], control mode switching [Koo-Pappas-Sastry]Computer Science: algorithmic synthesis [Maler et.al., Wong-Toi], synthesis based on HJB [Mitchell-Tomlin]

28

Hybrid Systems

29

Hybrid SystemsHybrid Automata (Lygeros-Tomlin-Sastry, 2001)

Ref: J. Lygeros, C. Tomlin, and S. Sastry, The Art of Hybrid Systems, July 2001.

30

Invariant set A

Invariant set B

Guard AB

Reset AB

Hybrid Systems

Q

X

Enabled Discrete Evolution

31

Invariant set A

Invariant set B

Guard AB

Reset AB

Hybrid Systems

Q

X

Forced Discrete Evolution

32

Hybrid Systems

33

ThermostatNon-deterministic Hybrid Automaton

t

34

Motivating Examples:Two Tanks

35

Zeno—infinitely many jumps in finite time

If

Water Tank Automaton

36

Motivating Examples: Bouncing BallZeno Hybrid Autamaton

37

Computational Tools

SimulationPtolemy II: ptolemy.eecs.berkeley.eduModelica: www.modelica.orgSHIFT: www.path.berkeley.edu/shiftDymola: www.dynasim.seOmSim: www.control.lth.se/~cace/omsim.htmlABACUSS: yoric.mit.edu/abacuss/abacuss.htmlStateflow: www.mathworks.com/products/stateflowCHARON: http://www.cis.upenn.edu/mobies/charon/Masaccio:

http://www-cad.eecs.berkeley.edu/~tah/Publications/masaccio.html

38

Computational Tools

Simulation

Models of Computation

System Complexity

Ptolemy II

DymolaModelica

ABACUSS

SHIFT

OmSim

MasaccioCHARON

StateFlow/Simulink

39

VerificationDeductive Methods

Theorem-Proving techniques [Lynch, Manna, Pnuelli]Model Checking

State-space exploration [Alur-Henzinger, Sifakis, Pappas-Lafferrier-Sastry]

XS

XF

Post(XS)

Post(P) = {x ∈ X|∃x0 ∈ P ∃t õ 0 s.t. x = þ(t, ri, x0)}

Check if Post(XS) ∩XF = ∅ ?

Forward Reachable Set

Reachability Problem

40

Computational Tools – Hybrid Systems

Reach Sets ComputationFiniteAutomata

TimedAutomata

LinearAutomata

LinearHybrid Systems

NonlinearHybrid Systems

d/dtCheckMate

Timed COSPANKRONOSTimed HSISVERITIUPPAAL

HYTECHCOSPANSMVVIS…

Requiem

xç = 1 Axç ô b xç = Ax xç = f(x)

S i(ri)S j(rj)

Prei(S j(rj), ri)

41

Research Directions

Hybrid SystemsEmbedded SoftwareHigh-Confidence Embedded SystemsNetwork-Centric Distributed Systems

Development of formal methods for the design of high-confidence embedded software based on hybrid system theory with applications to distributed, network-centric, embedded systems such as sensor networks, power electronics circuits, and cooperative UAV systems

42

Research CollaborationInstitutions

Center for Hybrid and Embedded Systems and Software (CHESS), University of California at BerkeleyGRASP Laboratory, University of PennsylvaniaHybrid Systems Laboratory, Stanford UniversityControl Group, Cambridge UniversityINRIA, FranceKTH, SwedenHoneywell LaboratoriesCadence Berkeley Laboratory

ConferencesWorkshop on Hybrid Systems: Computation and Control (HSCC)Workshop on Embedded Software (EMSOFT)IEEE Conference on Decision and Control (CDC)IEEE Conference on Robotics and Automation (ICRA)…

International Workshop on Hybrid Systems: Computation and Control

University of PennsylvaniaMarch, 2004

http://www.seas.upenn.edu/hybrid/HSCC04/

44

End