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EECE 396-1 Hybrid and Embedded Systems: Computation

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.koo@vanderbilt.edu

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EECE 396-1 Hybrid and Embedded Systems: Computation

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  1. 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 Hall February 12, 2004 john.koo@vanderbilt.edu http://www.vuse.vanderbilt.edu/~kootj All rights reserved.

  2. Analysis: Reachability - Continuous

  3. Topics • Definitions • Ordinary Differential Equations • Reachable Sets • Computation of Reachable Sets • Computational tools • Ref: • [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 11th Annual IEEE Symposium on Logic in Computer Science, pp. 278-292, 1996.

  4. Hybrid Automaton • Hybrid Automaton (Lygeros, 2003)

  5. Hybrid Automaton

  6. Hybrid Automaton Execution Q X

  7. Hybrid Automaton

  8. Ordinary Differential Equations

  9. Ordinary Differential Equations

  10. Ordinary Differential Equations

  11. Reachable Sets

  12. Reachable Sets

  13. Reachable Sets

  14. Reachable Sets

  15. Reachable Sets

  16. Reachable Sets

  17. Computation of Reachable Sets

  18. Computation of Reachable Sets

  19. Computation of Reachable Sets

  20. Computation of Reachable Sets

  21. Computation of Reachable Sets

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

  23. End

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