Supervisory Control of PDESs Based on Bisimulation Relations

In this paper, we study supervisory control of a nondeterministic systems -- probabilistic discrete event systems. As language equivalence is not an adequate notion of behavioral equivalence for some nondeterministic systems, here we use the finest known notion of equivalence: bisimulation equivalence. The design of a supervisor such that the controlled system is bisimilar to the specification is studied and a model theorem obtained, in which it shows that a supervisor exists if and only if it exists over a certain finite state space. Also, notions about state-controllability are introduced as part of a necessary and sufficient condition for the existence of the supervisor.