A method for the modular synthesis of controllers for timed discrete-event systems

A method for the modular supervisory control of timed discrete-event systems (TDES) is presented. The modular synthesis method is an extension of the centralized synthesis method proposed in our earlier work. We consider a state predicate specification as a conjunction of several state subpredicate specifications. The control problem is to synthesize a modular controller, the conjunction of all individual controllers, in such a way that the closed-loop behaviour of TDES satisfies the state predicate specification. Our modular synthesis method is developed based on the concept of state space of TDES, the notion of control-invariant state predicates for the TDES and a fixed point algorithm to calculate a control-invariant state subpredicate of a given state predicate. In addition, for the development of our modular synthesis method, we introduce the notion of control-invariance non-conflict among control-invariant state predicates, and the notion of forcing-non-conflict among controllers synthesized based on control-invariant state predicates which are control-invariance non-conflicting. The modular synthesis method in general offers better design flexibility and may require fewer computations than the centralized one. As in our centralized synthesis method, the proposed modular synthesis method does not require the construction and examination of complete sequences of event trajectories of the system. It is suggested that the computation of our proposed method of yielding solutions for a class of synthesis problems in TDES can be economical.