Non-blocking supervision for uncertain discrete event systems with internal unobservable transitions

A nonblocking supervisory control problem for uncertain discrete event systems (DESs) is considered, in which a Δ-transition describes the behaviour caused by internal and unobservable events. It is assumed that at a state with the assigned positive integer value p, a system experiences at most a p-step state transition by Δ. However, for some states, the internal and unobservable events may occur but the assigned positive integer values for the states are not known exactly. For the uncertain DESs, it is shown that they can be represented as a set of some non-deterministic models. Specifically, this paper presents necessary and sufficient conditions for the existence of a robust and non-blocking supervisor that achieves a given specification language for any model in the set. Moreover, when a given specification language does not satisfy the developed existence conditions, a supervisor synthesis problem is addressed to find the supremal sublanguage of the specification satisfying the conditions.