Control using nondeterministic supervisors for partially observed discrete event systems

Decentralized nondeterministic supervisory control of discrete event systems

“…On the other hand, coachievability is not preserved under union. This is in contrast to achievability (which has been shown to be preserved under union in [11]), implying that the decentralized control problems are inherently more dif£cult than the centralized ones. This dif£culty is also witnessed in the papers reporting undecidability of the decentralized estimation and control problems [14], [33].…”

“…Further, the form in which the condition of achievability was de£ned, it allowed the separation of limitations caused by "partialcontrol" and partial-observation. This paper extends the work in [11] from the centralized setting to the decentralized setting with the rule for decision fusion being based on conjunction (an event is enabled if and only if all supervisors having control over the event enable it). A deterministic (resp., nondeterministic) control policy can be represented a (Σ u , M)-compatible deterministic…”

“…Inan [5] £rst advocated the use of nondeterministic supervisors for control under partial observation. Recently, Kumar et al [11] proposed the notion of achievability to capture properties of more general nondeterministic supervisors, where "change in control action without any new observation", and nonprojection type observation masks are allowed. Further, the form in which the condition of achievability was de£ned, it allowed the separation of limitations caused by "partialcontrol" and partial-observation.…”

“…Σ ucompatibility requires that no uncontrollable event can be disabled at any state of the supervisor, and M -compatibility requires that any pair of indistinguishable events de£ned at a certain state must have the the same set of successor states. The notion of (Σ u , M)-achievability was introduced in [11] to characterize the class of languages that can be enforced as the controlled behavior by (Σ u , M)-compatible nondeterministic supervisors. It was shown that achievability is a weaker condition than controllability and observability combined, which serves as a necessary and suf£cient condition for the existence of deterministic control [17], [4].…”

“…Nondeterministic supervisory control under partial observation was proposed by Kumar et al [11] by allowing nondeterminism in control policies, which lead to the existence condition of achievability that is weaker than controllability and observability combined and is algebraically better behaved. In this paper, we extend nondeterministic control to the decentralized setting.…”