A New Supervisor Synthesis Approach for Discrete-Event Systems With Infinite Behavior

w-closure (together with w-controllability) plays an important role in the supervisor synthesis for liveness specifications imposed on discrete-event systems (DESs) with infinite behavior. However, it is not closed under arbitrary unions, and thus there does not exist the supremal w-closed (and w-controllable) sublanguage. In this paper, we first develop an algorithm to compute a subautomaton of the automaton representing an arbitrarily given w-language by deleting all bad loops (which lead to un-closedness of the given language) in the automaton, and show that the obtained subautomaton represents an w-closed sublanguage and is maximal from the perspective of an automaton transition graph. With this algorithm, we propose a new approach to construct a supervisor synthesizing an w-language even if it is not w-closed. Furthermore, we prove that, compared with the supervisor computed by the Thistle's supervisor synthesis approach, the supervisor synthesized by our approach is often more permissive. Examples are presented for illustration.