In networked control systems, uncontrollable events may unexpectedly occur in a plant before a proper control action is applied to the plant due to communication delays. In the area of supervisory control of discrete event systems, Park and Cho [5] proposed the notion of delay-nonconflictingness for the existence of a supervisor achieving a given language specification under communication delays. In this paper, we present the algebraic properties of delay-nonconflicting languages which are necessary for solving supervisor synthesis problems under communication delays. Specifically, we show that the class of prefix-closed and delay-nonconflicting languages is closed under intersection, which leads to the existence of a unique infimal prefix-closed and delay-nonconflicting superlanguage of a given language specification.

This paper addresses a robust supervisory control problem for uncertain timed discrete event systems (DESs) modeled as a set of some possible timed models. To avoid the state space explosion problem caused by tick transitions in timed models, the notion of eligible time bounds is presented. Based on the notion and activity (logical) models, this paper shows how the controllability condition of a given language specification is presented as a necessary and sufficient condition for the existence of a robust supervisor to achieve the specification for any timed model in the set.