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ESE601: Hybrid Systems

This review material explores examples, transition systems, languages, reachability, blocking property, automata composition, and I/O automata in the context of hybrid systems and discrete event systems.

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ESE601: Hybrid Systems

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  1. ESE601: Hybrid Systems Review material on discrete event systems I

  2. Contents • Examples (5) • Transition systems and automata (6) • Languages and regular expression (6) • Reachability and blocking property (5) • Composition of automata (5) • I/O automata (5)

  3. A vending machine • Insert coin(s) • Choose tea or coffee • Put the cup on the tray • Drink is ready ready cup tea coin coffee cup

  4. Printer data buffer Data in out in in out in out printer Data out overflow in

  5. jam fix out print ready A printer The printer receives data from the buffer, and print it out. Once the printout is ready, the printer is ready to receive new data. While printing, the paper can jam and need to be fixed before the printing process can resume.

  6. A slot machine • Insert coin • Pull handle • Win if the combination is good, otherwise lose. 7 7 7 7 7 win handle coin handle lose

  7. Modeling recap • Events are time-abstract. • Just like modeling of continuous systems, the level of detail is ‘modeler dependent’. • Events are not necessarily equipped with any notion of ‘internal-external’ or ‘input-output’. • Compositionality is possible (to be discussed later). • There can be non-determinism.

  8. Transition systems

  9. Transition systems 4 jam fix out 1 2 print 3 ready

  10. Execution of transition systems

  11. Automata

  12. Automata 4 jam fix out 1 2 print 3 ready

  13. Execution of automata

  14. Regular languages

  15. Regular languages

  16. Regular languages

  17. Regular languages

  18. Regular expressions

  19. Accessibility

  20. Blocking property

  21. Co-accessibility

  22. Co-accessibility

  23. Composition of automata

  24. Composition of automata a b 1,1 2,2 1,3 1 1 a a a b a a a 3 a 1,2 2,3 2,1 2 2 b

  25. Composition of automata

  26. Composition of automata

  27. Composition of automata out in 4 jam in out out 1 2 print 3 in out ready overflow in

  28. Composition and languages

  29. a a b c 1,1 2,1 3,2 5,1 d 4,2 Example 1 a 1 2 c a c b b d 3 4 2 c Only accessible states b 5

  30. Composition and languages

  31. Input – output automata

  32. Input – output automata

  33. Input – output automata

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