Deterministic supervisory control with flexible upper-bounds on observation delay and control delay

This paper considers supervisory control of discrete event systems with observation delay and control delay. We first extend the formulation of networked supervisory control in the literature by allowing both the upper bound of observation delay and the upper bound of control delay to vary among different event strings, and accommodating dynamic observation in which the past influences whether or not an occurrence of an event is observable. We then combine observation delay and control delay and prove that satisfying both controllability and delay observability over the combined delay is necessary and sufficient for the existence of a supervisor by which the desired language can be obtained deterministically. After that, we reduce the type of problems concerning the networked supervisory control to the corresponding type of problems concerning traditional supervisory control without any delay on observation or control. As an immediate application, the verifier of observability can be used to test the corresponding delay observability. Finally, this reduction is used to leverage methods for minimizing sensor activations for supervisory control without control delay to minimize sensor activations with control delay.