Bisimulation, the Supervisory Control Problem and StrongModel Matching for Finite State Machines

  • Authors:
  • George Barrett;Stéphane Lafortune

  • Affiliations:
  • Department of Electrical Engineering and Computer Science, The University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109–2122;Department of Electrical Engineering and Computer Science, The University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109–2122

  • Venue:
  • Discrete Event Dynamic Systems
  • Year:
  • 1998

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Abstract

Afundamental relationship between the controllability of a languagewith respect to another language and a set of uncontrollableevents in the Supervisory Control Theory initiated by (Ramadgeand Wonham, 1989) and bisimulation of automata models is derived.The theoretical results relating bisimulation to controllabilitysupport an efficient solution to the Basic Supervisory ControlProblem. Using (Fernandez, 1990) generalization of the partitionrefinement algorithm of (Paige and Tarjan, 1987), it is possibleto find a partition which represents the supremal controllablesublanguage of an automaton with respect to the language of anotherautomaton and a set of events in a worst-case running time ofO( m\log(n)), where m is the numberof transitions and n is the number of states. Utilizingthe bisimulation property of language controllability and derivedrelationships between automata languages and input/output finite-statemachine behaviors, a precise relationship is formally derivedbetween Supervisory Control Theory and the system-theoretic problemposed by (DiBenedetto et al., 1994) called Strong Input/OutputFSM Model Matching. Specifically, it is proven that in deterministicsettings instances of each problem can be mapped to the otherframework and solved.