EECE Hybrid 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 Hall January 29,

2 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)

3 Modeling: Timed Automata

4 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: , 1996.Automatic Symbolic Verification of Embedded Systems. [2] T.A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: A Model Checker for Hybrid Systems. Software Tools for Technology Transfer 1: , 1997.HyTech: A Model Checker for Hybrid Systems.

5 (Non-)Deterministic Finite Automata

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9 Ordering of events

10 Ordering of events

11 Ordering of events

12 Timed Automata

13 Timed Automata

14 Timed Automata

15 Timed Automata

16 Timed Automata

17 Timed Automata GPS INS

18 Timed Automata

19 Timed Automata

20 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

21 Train Gate model

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