Supervisor Synthesis for Networked Discrete Event Systems With Communication Delays

We investigate supervisory control of networked discrete event systems with asynchronous communication between the plant and supervisor. The observation and control may be randomly delayed. The delays are bounded and will not change the order of observation (FIFO). Our goal is to synthesize a supervisor such that the behavior of the supervised system is both adequate and legal (safe). We derive a necessary and sufficient condition for the existence of such a supervisor. When the condition is satisfied, we find a minimally-permissive state-estimate-based control policy which can be implemented offline or online. Furthermore, we derive an algorithm to check the condition for the existence of the supervisor by constructing an augmented automaton. The algorithm allows us to obtain a maximally-permissive control policy by iteration.