EECE 396-1 Hybrid and Embedded Systems: Computation

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 April 20 , 2004 john.koo@vanderbilt.edu http://www.vuse.vanderbilt.edu/~kootj

2. Summary

3. 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)

4. Why Hybrid Systems? • Modeling abstraction of • Continuous systems with phased operation (e.g. walking robots, mechanical systems with collisions, circuits with diodes) • Continuous systems controlled by discrete inputs (e.g. switches, valves, digital computers) • Coordinating processes (multi-agent systems) • Important in applications • Hardware verification/CAD, real time software • Manufacturing, communication networks, multimedia • Large scale, multi-agent systems • Automated Highway Systems (AHS) • Air Traffic Management Systems (ATM) • Uninhabited Aerial Vehicles (UAV) • Power Networks

5. Topics • Modeling • Finite State Machines • Time Automata • Ordinary Differential Equations • Hybrid Automata • Analysis • Reachability - Discrete • Reachability - Continuous • Reachability - Hybrid • Tool • Ptolemy II • HyTech • Requiem • d/dt • Checkmate • Verification • Temporal Logic • Model Checking • Time Automata

6. Hybrid Automaton

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

8. Hybrid Automaton Execution Q X

9. Examples: Thermostat

10. Examples: Bouncing Ball

11. Motivating Examples:Two Tanks

12. Hybrid Automaton i 4 3 2 1 0 t

13. Hybrid Automaton i 4 3 2 1 0 t

14. Hybrid Automaton i 4 3 2 1 0 t

15. Hybrid Automaton

16. Examples: Bouncing Ball

17. Hybrid Automaton i i 2 2 1 1 0 0 t t finite infinite

18. Hybrid Automaton i i 2 2 1 1 0 0 t t finite Zeno

19. Hybrid Automaton • Zeno of Elea, 490BC • Ancient Greek philosopher • The race of Achilles and the turtle • Achilles, a renowned runner, was challenged by the turtle to a race. Being a fair sportsman, Achilles decided to give the turtle a 10 meter head-start. To overtake the turtle, Achilles will have to first cover half the distance separating them. To cover the remaining distance, he will have to cover half that distance, and so on. • No matter how fast Achilles is, he can never overtake the turtle. Why??? • Ans: Covering each one of the segments in this series requires a non zero amount of time. Since there is an infinite number of segments, Achilles will never overtake the turtle.

20. Hybrid Automaton • Non-Determinism • Multiple Executions for the same initial condition • Sources of non-determinism • Non-Lipschitz continuous vectorfields, f • Multiple discrete transition destinations, E & G • Choice between discrete transition and continuous evolution, D & G • Non-unique continuous state assignment, R Definition: A hybrid automaton H is deterministic if for all initial conditions there exists a unique maximal sequence

21. Hybrid Automaton • Blocking • No Infinite executions for some initial states • Source of blocking • Cannot continue in domain due to reaching the boundary of the domain where no guard is defined • Have no place to make discrete transition to Definition: A hybrid automaton H is non-blocking if for every initial condition there exists at least one infinite execution ?

22. Hybrid Automaton • Zeno Executions • Infinite execution defined over finite time • Infinite number of transitions in finite time • Transition times converge Definition: A hybrid automaton H is zeno if there exists an initial condition for which all infinite executions are Zeno

23. Exercise

24. Examples: Bouncing Ball • Is this model: • Deterministics? • Non-Blocking? • Zeno?

25. Examples: Bouncing Ball • Is this model: • Deterministics? • Yes, the Guard and Domain contains only one element. Reset maps from one point to exactly another point. Also, the vector field is Lipschitz continuous. • Non-Blocking? • Zeno?

26. Examples: Bouncing Ball • Is this model: • Deterministics? • Non-Blocking? • Yes, the guard is always reachable from any initial condition within the domain and also the reset makes the state start within the domain. • Zeno?

27. Examples: Bouncing Ball

28. Examples: Bouncing Ball

29. Examples: Bouncing Ball

30. Examples: Bouncing Ball • Is this model: • Deterministics? • Non-Blocking? • Zeno? • Yes, it is Zeno since the time sequence converges.

31. Thermostat • Is this model: • Deterministics? • Non-Blocking? • Zeno?

32. Thermostat • Is this model: • Deterministics? No. • Non-Blocking? Yes. • Zeno? No.

33. Two Tanks • Is this model: • Deterministics? Yes. • Non-Blocking? Yes. • Zeno? Yes.

34. If Water Tank Automaton Zeno—infinitely many jumps in finite time

35. Timed Automata • Is this model: • Deterministics? • Non-Blocking? • Zeno?

36. Timed Automata • Is this model: • Deterministics? No. • Non-Blocking? Yes. • Zeno? No.

37. In Summary

38. In Summary Verification Special Attention in Simulation Mapping Verification

39. Computational Tools

40. Computational Tools • Simulation • Ptolemy II: ptolemy.eecs.berkeley.edu • Modelica: www.modelica.org • SHIFT: www.path.berkeley.edu/shift • Dymola: www.dynasim.se • OmSim: www.control.lth.se/~cace/omsim.html • ABACUSS: yoric.mit.edu/abacuss/abacuss.html • Stateflow: www.mathworks.com/products/stateflow • CHARON: http://www.cis.upenn.edu/mobies/charon/ • Masaccio: http://www-cad.eecs.berkeley.edu/~tah/Publications/masaccio.html

41. Computational Tools • Simulation Masaccio CHARON Ptolemy II Dymola Modelica StateFlow/Simulink System Complexity ABACUSS SHIFT OmSim Models of Computation

42. Computational Tools • Verification 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

43. End