Enforcing Detectability in Controlled Discrete Event Systems

In this technical note, we investigate supervisory control that enforces strong detectability and strongly periodic detectability in a discrete event system. The goal of control is to ensure that the current state of the closed-loop system can be determined forever or periodically after some finite observations for all trajectories of the system. We derive necessary and sufficient conditions for the existence of supervisory control and develop algorithms to synthesize such supervisors if they exist.