Hybrid Embedded Timed Automata Analysis 2004
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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 Featheringil l Hall April 6-15, 2004
john.koo@vanderbilt.edu
http://www.vuse.vanderbilt.edu/~kootj
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Analysis: Timed Automata
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Topics Bisimular Transition Systems
Transition Systems
Forward and Backward Reachability Algorithms
Simulation and Bisimulation Relations
Transition Systems and Quotient Transition Systems
Bisimulation between Transition Systems
Bisimulation Algorithm
Bisimulations of Timed Automata
Executions of Timed Automata
Region Equivalent Relation and Parti tion
Ref:
[1] R. Alur, T.A. Henzinger, and P.-H. Ho. Automatic Symbolic Verificationof Embedded Systems. IEEE Transactions on Software Engineering22:181-201, 1996.
[2] J. Lygeros, Lecture Notes on Hybrid Systems, Cambridge, 2003. [3] J. Lygeros, C. Tomlin, and S. Sastry, The Art of Hybrid Systems, July
2001.
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Analysis: Timed AutomataBisimular Transition Systems
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Transition System
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Transition System
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Transition System
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Transition System
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Forward and Backward
Reachability Algorithms
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Forward and Backward
Reachability Algorithms
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Forward and Backward
Reachability Algorithms
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Forward and Backward
Reachability Algorithms
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Simulation and Bisimulation
Relations
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Bisimulation Algorithm
How?
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Bisimulation Algorithm
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Analysis: Timed AutomataBisimulations of 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
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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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Hybrid Automaton
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Hybrid Automaton
i
0
1
2
tfinite
i
0
1
2
tinfinite
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Hybrid Automaton
i
0
1
2
tfinite
i
0
1
2
tZeno
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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 transit ion to
Definition: A hybrid automaton H is non-blocking if for every
initial condition there exists at least one infinite execution
?
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Hybrid Automaton Zeno Executions
Infinite execution defined over finite time
Infinite number of transitions in finite time
Transition t imes converge
Definition: A hybrid automaton H is zeno if there exists an
initial condition for which all infinite executions are Zeno
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Transition System
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Region Equivalence Relation
R i E i l R l ti
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Region Equivalence Relation
Ti d A t t
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Timed Automata
Ti d A t t
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Timed Automata
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Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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Region Equivalence Relation
Region Equivalence Relation
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eg o qu a e ce e at o
Region Equivalence Relation
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g q
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