Consistent abstractions for the purpose of supervisory control

Abstract

A common strategy in the design of discrete event systems is to run synthesis algorithms not on the actual plant model but on abstractions thereof. Depending on the control objectives, certain conditions are imposed on the abstractions, in order to end up with an appropriate supervisory controller for the actual plant. A well known result from the literature is that abstractions obtained by so called natural observers can be used for non-blocking supervisory control. In this paper, we conduct a backward-reachability analysis to obtain alternative conditions that imply a non-blocking and complete closed-loop system for an abstraction-based supervisory controller design.

Natural Projections for the Synthesis of Non-Conflicting Supervisory Controllers

“…In (Malik et al, 2007), it is shown that the observer property is not only sufficient but also necessary to obtain a conflict equivalent abstraction used for compositional non-blocking verification. The present paper is a further development of the reachability analysis presented in (Moor et al, 2013). In contrast to the earlier results, the novel condition obtained in the present paper is not only suffi-cient but also necessary for non-conflicting controller synthesis, i.e., we characterise precisely those projections, for which an abstraction-based controller design is guaranteed to exhibit a non-conflicting closed-loop behaviour.…”

“…The second and the third implication are consequences of the more general results given in (Zhong and Wonham, 1990), Theorem 4.1, and in (Wong and Wonham, 1996), Theorem 6, respectively. For a direct proof addressing the specific situation at hand, see also (Moor et al, 2013).…”

“…We interpret the characterisation of consistency by Theorem 7 in the context of the reachability analysis proposed in (Moor et al, 2013). The given reference presents sufficient conditions to identify strings from the local plant behaviour that, under supervision by any abstraction based controller, exhibit at least one extension that enters a given target language.…”

“…Consequences for the situation of regular languages are drawn in Section 5 to provide the basis for a software implementation. Finally, Section 6 interprets the results in the context of the reachability analysis proposed in (Moor et al, 2013).…”

Hierarchical modelling of manufacturing systems using discrete event systems and the conflict preorder

“…While these methods are not as structured as HISC, it is known that a projection that satisfies the observer property [25,42,43] can serve as an abstraction of a subsystem and thus as its interface. With additional requirements such as output control consistency [10] or local control consistency [30,35], it is also possible to ensure maximal permissiveness of supervisors when using synthesis. However, the observer property is a strong requirement, and it is not guaranteed that an interface exists for every given subsystem and choice of interface events [25].…”