A state-based reasoning for the supervisory control of timed discrete event systems

AbstmctIn this paper the problem of controlling the behavior of a given Time Discrete Event System (TDES) is approached in terms of predicate and predicate transformer. The Supervisory Control Problem (SCP) is introduced as the problem of synthesizing a supervisor for a given TDES. So that, the set of legal predicate corresponds to the weakest predicate that remains invariant and reachable nnder control. In contrast of the work 121, the approach proposed does not rely on a search through the entire reachability of the timed automaton of a given TDES. The notion ofcontrollability ofa predicate deRned in [9] is adapted. It is shown that predicate controllability serves as a necessary and sufficient condition for the existence of a state feedback controller which solves the SCP. To compute the suprema1 controllable predicate a fixpoint algorithm is proposed.