EECE 396-1Hybrid and Embedded Systems: Computation

T. John Koo

Institute for Software Integrated Systems

Department of Electrical Engineering and Computer Science

Vanderbilt University

300 Featheringill HallJanuary 14, 2004

john.koo@vanderbilt.edu

http://www.vuse.vanderbilt.edu/~kootj

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Hybrid Systems UC 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.html

Spring 1998 by Thomas A. Henzinger, S. Shankar Sastry Stanford University

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

University of Pennsylvania Fall 2000 by Rajeev Alur, George J. Pappas

http://www.seas.upenn.edu/~pappasg/EE601/

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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

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Hybrid System

Continuous systems with phased operations Bouncing ball Circuits with diodes Switching circuits

Continuous systems controlled by discrete inputs Thermostat Water tank Engine control systems Multi-modal systems Embedded control systems

q1q2

q3

u

xç = f (x) + g(x)u

x

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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

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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

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The Hierarchical View of Systems

controller

I C

H

car model

enginepowertrain

E

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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

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Embedded Systems

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

q1q2

q3

u

xç = f (x) + g(x)u

xD/A A/D

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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

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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 Altitude

Control outputat 50Hz

Nav data

DGPS measurement

Nav Data to Vision computer

@10Hz

RS-232

Shared Memory

Radio link

RX valuesRX valuesYamaha Receiver(using HW INT & proxy)

Ground computerWin 98

Processesrunning on QNX

4±1Hz10Hz

ANYTIME

APERIODIC

PERIODIC

PERIODIC

PERIODIC

High-Confidence Embedded Software

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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

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Different Approaches

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H ig h -C o n fid e n c e E m b e d d e d S y s te m s• C o rre c tn e ss b y c o n s tru c tio n

• F a u lt- to le ra n ce

• R e s is ta n ce to a tta c k

200 Hz 400

Hz

200 Hz

1 kHz

F lig h t C o n tro l S o ftw a re

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

N e tw o r k - C e n t r ic D is t r ib u te d S y s te m s• C o o p e r a t iv e C o n tro l o f M u lt ip le U A V s

• P o w e r E le c t ro n ic s C ir c u i ts

• S e n s o r N e tw o rk s

H y b r i d S y s t e m sC o n t r o l T h e o r y

C o n t r o l o f i n d i v i d u a l a g e n t sC o n t i n u o u s m o d e l sD i f f e r e n t i a l e q u a t i o n s

C o m p u t e r S c i e n c eM o d e l s o f c o m p u t a t i o nC o m m u n i c a t i o n m o d e l sD i s c r e t e e v e n t s y s t e m s

H y b r i d S y s t e m s

Research Directions

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What Are Hybrid Systems?

Dynamical systems with interacting continuous and discrete dynamics

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Proposed Framework

Control TheoryControl of individual agentsContinuous modelsDifferential equations

Computer ScienceModels of computationCommunication modelsDiscrete event systems

Hybrid Systems

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ENNA GmbH

Power Electronics Power electronics found in:

DC-DC converters Power supplies Electric 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)

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ENNA GmbH

Power Electronics Discrete dynamics

N switches, (up to) 2N discrete states Only discrete inputs (switching): some

discrete transitions under control, others not

Continuous dynamics Linear or affine dynamics at each discrete

state

+ +

23=8 possible configurations

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Power Electronics : DC-DC Converters

Have a DC supply (e.g. battery), but need a different DC voltage

Different configurations depending on whether Vin<Vout or Vin>Vout

Control switching to maintain Vout with changes in load (R), and Vin

Vin

L C Rsw1

sw2+

-

+

-

Vout

iL

iL

Vout

2 1 2

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Two Output DC-DC Converter

Want two DC output voltages Inductors are big and heavy, so

only want to use one Similar to “two tank” problem

Vin

L

C2 R2sw1

sw2+

-

+

-

VoutA

iL+

-

VoutB

sw3

C3 R3

iL

VoutA

VoutB

1 2 3 1 2 3

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Circuit Operation

One and only one switch closed at any time

Each switch state has a continuous dynamics

sw1: iL, VoutA, VoutB

sw2: iL , VoutA , VoutB sw3: iL , VoutA, VoutB

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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

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Typical Circuit Analysis/Control

Governing equations Time domain, steady state Energy balance

System dynamics Discretization in time

Switched quantity only sampled at discrete instants

Assumes a fixed clock Averaging

Switched quantity approximated by a moving average

Assumes switching is much faster than system time constants

Control Linearize with duty () as input Use classical control techniques

T

T (1- )T

i0

i1

i2

match!

iL(t)iL(t)

iL[k]

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Outline

Background on Power Electronics Hybrid Modeling of DC-DC Converters Controlled Invariant Balls Conclusions

Vin

L C Rsw1

sw2+

-

+

-Vout

iL

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Problem Formulation

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q1

xç(t) = f q1(x(t))x(t) 2 I q1

q2

xç(t) = f q2(x(t))x(t) 2 I q2

û = û2

û = û1

q1

û = û1

q2

û = û2

x 2 G12

x 2 G21

û 2 Î

x 2 X

H1

H2

Problem Formulation Parallel Composition of Hybrid

Automata

Given a collection of Modes and Edges, design Guards

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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 & Verification Control: 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 Synthesis Control: 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]

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Hybrid Systems

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Hybrid Systems

Hybrid Automata (Lygeros-Tomlin-Sastry, 2001)

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

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Invariant set A

Invariant set B

Guard AB

Reset AB

Hybrid Systems

Q

X

Enabled Discrete Evolution

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Invariant set A

Invariant set B

Guard AB

Reset AB

Hybrid Systems

Q

X

Forced Discrete Evolution

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Hybrid Systems

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Motivating Examples: ThermostatNon-deterministic Hybrid Automaton

t

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Motivating Examples:Two Tanks

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Zeno—infinitely many jumps in finite time

If

Water Tank Automaton

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Motivating Examples: Bouncing BallZeno Hybrid Autamaton

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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

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Computational Tools

Simulation

Models of Computation

System Complexity

Ptolemy II

DymolaModelica

ABACUSS

SHIFT

OmSim

MasaccioCHARON

StateFlow/Simulink

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Verification Deductive Methods

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

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

X S

X F

Post(X S)

Post(P) = fx 2 Xj9x0 2 P 9t õ 0 s:t: x = þ(t;ri;x0)g

Check if Post(X S) \ X F = ; ?

Forward Reachable Set

Reachability Problem

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Computational Tools – Hybrid Systems

Reach Sets ComputationFiniteAutomata

TimedAutomata

LinearAutomata

LinearHybrid Systems

NonlinearHybrid Systems

d/dtCheckMate

Timed COSPANKRONOSTimed HSISVERITIUPPAAL

HYTECHCOSPANSMVVIS…

Requiem

xç= 1 Axçô b xç= Ax xç= f (x)

Si(r i)Sj(r j)

Prei(Sj(r j);r i)

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Research Directions

Hybrid Systems Embedded Software High-Confidence Embedded Systems Network-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

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Research Collaboration

Institutions Center for Hybrid and Embedded Systems and Software (CHESS),

University of California at Berkeley GRASP Laboratory, University of Pennsylvania Hybrid Systems Laboratory, Stanford University Control Group, Cambridge University INRIA, France KTH, Sweden Honeywell Laboratories Cadence Berkeley Laboratory

Conferences Workshop 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/

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End