Mutually Nonblocking Supervisory Control

For discrete event systems, modular supervisory control refers to modular design of a supervisor when multiple control specifications are given. This problem has been studied for the case when the desired specifications must all simultaneously be met. In this paper, we study the case when at least one of the desired specifications must always be met while never blocking any of the remaining specifications. In addition, the entire controlled system must be nonblocking. Thus, we study the case of “disjunction” (as opposed to “conjunction” as in prior work) with the provision for ensuring a type of fairness with regards to each individual specification. We call this the problem of mutually nonblocking supervision, which is demonstrated to have applications in feature interactions in telephony, protocol conversion, and manufacturing. We present a necessary and sufficient condition for the existence of a mutually nonblocking supervisor, where the relevance of the notion of mutual prefix-boundedness is established. Next we show the existence of a maximally permissive mutually nonblocking supervisor, and provide a closed-form formula of the behavior that is achieved under its supervision whenever the desired specification languages are weakly nonconflicting. The formula turns out to be the union of the supremal prefix-bounded sublanguage of one specification language with respect to another. We end by demonstrating that the problem we address is equivalent to the problem of “multiply nonblocking supervision” studied by Lafortune et al. and Thistle et al., and so the techniques developed here can be applied there and vice-versa.