Existence Conditions of State Feedback in Discrete Event Systems under Partial State Observation

Abstract

In this paper, we consider state feedback control of discrete event systems under partial state observation. A control specification is assumed to be given in terms of a predicate on the set of states. First, we introduce a new definition of observability of predicates, which is a generalization of the definition proposed by Li and Wonham. We then show necessary and sufficient conditions for the existence of a state feedback which achieves the control specification. Next, we introduce the notion of η-observability, which is a natural extention of observability, and present necessary and sufficient conditions for the existence of a decentralized state feedback which achieves the control specification.