EECE 396-1 Hybrid and Embedded Systems: Computation

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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_at_vanderbilt.edu
• http//www.vuse.vanderbilt.edu/kootj

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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)

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Modeling Timed Automata
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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 22181-201, 1996.
• 2 T.A. Henzinger, P.-H. Ho, and H. Wong-Toi.
  HyTech A Model Checker for Hybrid Systems.
  Software Tools for Technology Transfer 1110-122,
  1997.

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(Non-)Deterministic Finite Automata
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(Non-)Deterministic Finite Automata
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(Non-)Deterministic Finite Automata
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(Non-)Deterministic Finite Automata
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Ordering of events
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Ordering of events
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Ordering of events
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Timed Automata
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Timed Automata
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Timed Automata
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Timed Automata
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Timed Automata
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Timed Automata
GPS
INS
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Timed Automata
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Timed Automata
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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

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Train Gate model
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End