Predicates and predicate transformers for the supervisory control of timed discrete event system

We approach the problem of controlling the behavior of a given real time discrete event system (RTDES) described in terms of its state trajectories by using predicates and predicate transformers. The timed supervisory predicate control problem (TSPCP) is introduced as the problem of synthesizing a supervisor for a given RTDES. So that, the set of legal predicates corresponds to the weakest predicate that remains invariant under control. RTDES is modeled as a finite automaton and characterized by its untimed automaton, namely the activity transition graph augmented by data variables, and its timed automaton, namely its timed transition graph. In contrast to the work of Brandin (1994) and O'Young (1991), the approach proposed in the paper does not rely on a search through the reachability of the timed automaton of a given RTDES. The TSPCP addressed in the paper takes into account two types of control mechanisms: enabling/disabling and forcing events. Furthermore two types of controllability notion are handled. The first one corresponds to the classical notion of controllability when the forcing mechanism is not invoked, and it is shown that it serves as a necessary and sufficient condition for solving the TSPCP. The second one is called forced controllability and used to solve the TSPCP in the case where the required legal predicate is not controllable.