Supervisory control of partially observed discrete event systems with arbitrary control patterns

In this paper, we study supervisory control of partially observed discrete event systems with arbitrary control patterns. First, we present a necessar y and sufficient condition for the existence of a supervisor for a given no n-empty and closed language K. Next, rue consider the case where the langua ge K does not satisfy the condition. We prove that there always exists its infimal superlanguage for which there exists a supervisor when the set Gamm a of control patterns is closed under intersection. This infimal superlangu age is the optimal solution larger than K. On the other hand when Gamma is closed under union, there does not necessarily exist its supremal sublangua ge for which there exists a supervisor. In other words, the optimal solutio n smaller than K does not exist in general. So, in this case, we present a suboptimal solution smaller than K.