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 January 29, 2004 john. koo@vanderbilt. edu http: //www. vuse. vanderbilt. edu/~kootj
Hybrid System n A system built from atomic discrete components and continuous components by parallel and serial composition, arbitrarily nested. n The behaviors and interactions of components are governed by models of computation (MOCs). n Discrete Components n Finite State Machine (FSM) n Discrete Event (DE) n Synchronous Data Flow (SDF) n Continuous Components n Ordinary Differential Equation (ODE) n Partial Differential Equation (PDE)
Modeling: Timed Automata
Topics n Finite Automata n Transition Relation = Edges + Guard n Ordering of events n Timed Automata n Notions of time: Global/Local Clocks n Transition Relation n Total ordering of events n Multi-rate time automata n Example n Rate Monotonic Scheduling n Train Gate model n Ref: n [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. n [2] T. A. Henzinger, P. -H. Ho, and H. Wong-Toi. Hy. Tech: A Model Checker for Hybrid Systems. Software Tools for Technology Transfer 1: 110 -122, 1997.
(Non-)Deterministic Finite Automata
(Non-)Deterministic Finite Automata
(Non-)Deterministic Finite Automata
(Non-)Deterministic Finite Automata
Ordering of events
Ordering of events
Ordering of events
Timed Automata
Timed Automata
Timed Automata
Timed Automata
Timed Automata
Timed Automata GPS INS
Timed Automata
Timed Automata
Train Gate model n 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. Hy. Tech computes the safe values of a such that the gate is fully closed whenever the train is within 10 meters of the gate. n Reference and On-Line Demo: n www-cad. eecs. berkeley. edu/~tah/Hy. Tech/demo. html
Train Gate model
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