On algebraic properties of delay-nonconflicting languages in supervisory control under communication delays

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 gven language specification under communication delays. In this paper, we present the algebraic properties of delay-nonconflicting languages whch are necessary for solving supervisor synthesis problems under communcation 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-nonconctng superlanguage of a given language specification.