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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 5, 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 5, 2004 john.koo@vanderbilt.edu http://www.vuse.vanderbilt.edu/~kootj

  2. 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)

  3. Modeling: Hybrid Automata

  4. Topics • Hybrid Automata • Definitions • Examples • Bouncing Ball • Thermostat • Properties • Executions • Non-Determinism • Blocking • Zeno Executions • 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.

  5. 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

  6. Control Theory Computer Science Models of computation Control of individual agents Communication models Continuous models Discrete event systems Differential equations Hybrid Systems Proposed Framework

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

  8. Hybrid Automaton

  9. Hybrid Automaton Execution Q X

  10. Examples: Bouncing Ball

  11. HyVisual http://ptolemy.eecs.berkeley.edu http://ptolemy.eecs.berkeley.edu/ptolemyII/hyvisual2.2/

  12. Examples: Bouncing Ball

  13. Examples: Bouncing Ball

  14. Examples: Bouncing Ball

  15. Hybrid Automaton i 4 3 2 1 0 t

  16. Hybrid Automaton i 4 3 2 1 0 t

  17. Hybrid Automaton i 4 3 2 1 0 t

  18. Hybrid Automaton

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

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

  21. 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.

  22. 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

  23. Examples: Thermostat

  24. 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 ?

  25. 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

  26. Examples: Bouncing Ball

  27. End

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