Synthesis of decentralized state feedbacks for large‐scale discrete event systems
Shigemasa Takai, Shinzo Kodama, Toshimitsu Ushio · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1994
Abstract This paper considers the large‐scale discrete event system which is composed of multiple concurrently operating subsystems. The decentralized state feedback control is discussed for the case where the control specifications are given by predicates concerning the whole system. First, a necessary and sufficient condition is shown for a predicate which is obtained by a global state feedback to be obtained also by a decentralized state feedback. However, it should be noted that, in general, there exists more than one decentralized state feedback that can achieve the global predicate. From such a viewpoint, the maximally and minimally permissive decentralized feedbacks are defined and investigated. It is shown that there always exists the minimally permissive decentralized feedback, and its construction method is presented. Also, it is shown that, although the maximally permissive decentralized feedback does not, in general, exist, it can be obtained in the case that local state feedbacks are constructed according to a specified order. The construction method for that case is shown.