1. 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 10, 2004 john.koo@vanderbilt.edu http://www.vuse.vanderbilt.edu/~kootj

2. 2 Analysis: Reachability - Discrete

3. 3 Topics Definitions Transition System Reachable Sets Reachability Problem Reachability Algorithm Decidability 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. 4 Hybrid Automaton Hybrid Automaton (Lygeros, 2003)

5. 5 Hybrid Automaton

6. 6 Q X Execution

7. 7 Transition System

8. 8 Unsafe Set Transition System Initial set

9. 9 Unsafe Set Transition System Initial set

10. 10 Transition System

11. 11 Transition System

12. 12 Transition System

13. 13 Transition System

14. 14 Transition System

15. 15 Transition System

16. 16 Transition System

17. 17 Transition System

18. 18 Transition System

19. 19 Transition System

20. 20 Transition System

21. 21 Transition System

22. 22 Transition System

23. 23 Transition System Unsafe!!

24. 24 Transition System Safe!!

25. 25 Transition System Keep iterating until when!?

26. 26 Transition System

27. 27 Transition System

28. 28 Transition System Keep iterating until when!?

29. 29 Transition System Keep iterating until when!?

30. 30 Transition System Keep iterating until when!?

31. 31 End