EECE 396 1 Hybrid and Embedded Systems Computation

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EECE 396 -1 Hybrid and Embedded Systems: Computation T. John Koo, Ph. D. Institute

EECE 396 -1 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 February 12, 2004 john. [email protected] edu http: //www. vuse. vanderbilt. edu/~kootj All rights reserved.

Analysis: Reachability - Continuous

Analysis: Reachability - Continuous

Topics n Definitions n Ordinary Differential Equations n Reachable Sets n Computation of Reachable

Topics n Definitions n Ordinary Differential Equations n Reachable Sets n Computation of Reachable Sets n Computational tools n Ref: n n n [1] J. Lygeros, Lecture Notes on Hybrid Systems, Cambridge, 2003. [2] J. Lygeros, C. Tomlin, and S. Sastry, The Art of Hybrid Systems, July 2001. [3] Thomas A. Henzinger , The theory of hybrid automata, Proceedings of the 11 th Annual IEEE Symposium on Logic in Computer Science, pp. 278 -292, 1996.

Hybrid Automaton n Hybrid Automaton (Lygeros, 2003)

Hybrid Automaton n Hybrid Automaton (Lygeros, 2003)

Hybrid Automaton

Hybrid Automaton

Hybrid Automaton Execution Q X

Hybrid Automaton Execution Q X

Hybrid Automaton

Hybrid Automaton

Ordinary Differential Equations

Ordinary Differential Equations

Ordinary Differential Equations

Ordinary Differential Equations

Ordinary Differential Equations

Ordinary Differential Equations

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computation of Reachable Sets

Computational Tools n Reachable Sets Computation Finite Automata COSPAN SMV VIS … Timed Automata

Computational Tools n Reachable Sets Computation Finite Automata COSPAN SMV VIS … Timed Automata Timed COSPAN KRONOS Timed HSIS VERITI UPPAAL Linear Automata HYTECH Linear Hybrid Systems Requiem Nonlinear Hybrid Systems d/dt Check. Mate

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