EECE 396-1Hybrid and Embedded Systems: Computation

T. John Koo, Ph.D.

Institute for Software Integrated Systems

Department of Electrical Engineering and Computer Science

Vanderbilt University

300 Featheringill HallJanuary 29, 2004

john.koo@vanderbilt.edu

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

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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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Modeling: Timed Automata

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Topics Finite Automata

Transition Relation = Edges + Guard Ordering of events

Timed Automata Notions of time: Global/Local Clocks Transition Relation Total ordering of events Multi-rate time automata

Example Rate Monotonic Scheduling Train Gate model

Ref: [1] R. Alur, T.A. Henzinger, and P.-H. Ho.

Automatic Symbolic Verification of Embedded Systems. IEEE Transactions on Software Engineering 22:181-201, 1996.

[2] T.A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: A Model Checker for Hybrid Systems. Software Tools for Technology Transfer 1:110-122, 1997.

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(Non-)Deterministic Finite Automata

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(Non-)Deterministic Finite Automata

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(Non-)Deterministic Finite Automata

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(Non-)Deterministic Finite Automata

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Ordering of events

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Ordering of events

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Ordering of events

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Timed Automata

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Timed Automata

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Timed Automata

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Timed Automata

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Timed Automata

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Timed Automata

GPS

INS

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Timed Automata

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Timed Automata

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Train Gate model The gate controller of a railroad crossing has a delay of

a seconds; that is, the gate starts closing a seconds after a train signals its approach. HyTech computes the safe values of a such that the gate is fully closed whenever the train is within 10 meters of the gate.

Reference and On-Line Demo: www-cad.eecs.berkeley.edu/~tah/HyTech/demo.html

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Train Gate model

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End