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Understanding Hybrid and Embedded Systems: Fundamentals and Applications

This document, authored by Dr. John Koo of Vanderbilt University, provides an in-depth exploration of hybrid and embedded systems, emphasizing the integration of discrete components (like Finite State Machines and Synchronous Data Flow) with continuous components (such as Ordinary and Partial Differential Equations). Key concepts include different types of models of computation, detailed analysis of timed automata, and applications like rate monotonic scheduling. The document also references significant works and tools in the field, such as HyTech, a model checker for hybrid systems.

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Understanding Hybrid and Embedded Systems: Fundamentals and Applications

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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 January 29, 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: Timed Automata

  4. Topics • Finite Automata • Transition Relation = Edges + Guard • Ordering of events • Timed Automata • Notions of time: Global/Local Clocks • Transition Relation • Total ordering of events • Multi-rate time automata • Example • Rate Monotonic Scheduling • Train Gate model • Ref: • [1] R. Alur, T.A. Henzinger, and P.-H. Ho. Automatic Symbolic Verification of Embedded Systems. IEEE Transactions on Software Engineering 22:181-201, 1996. • [2] T.A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: A Model Checker for Hybrid Systems. Software Tools for Technology Transfer 1:110-122, 1997.

  5. (Non-)Deterministic Finite Automata

  6. (Non-)Deterministic Finite Automata

  7. (Non-)Deterministic Finite Automata

  8. (Non-)Deterministic Finite Automata

  9. Ordering of events

  10. Ordering of events

  11. Ordering of events

  12. Timed Automata

  13. Timed Automata

  14. Timed Automata

  15. Timed Automata

  16. Timed Automata

  17. Timed Automata GPS INS

  18. Timed Automata

  19. Timed Automata

  20. Train Gate model • The gate controller of a railroad crossing has a delay of a seconds; that is, the gate starts closing a seconds after a train signals its approach. HyTech computes the safe values of a such that the gate is fully closed whenever the train is within 10 meters of the gate. • Reference and On-Line Demo: • www-cad.eecs.berkeley.edu/~tah/HyTech/demo.html

  21. Train Gate model

  22. End

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