Reliable Decentralized Control of Fuzzy Discrete-Event Systems and a Test Algorithm

A framework for decentralized control of fuzzy discrete-event systems (FDESs) has been recently presented to guarantee the achievement of a given specification under the joint control of all local fuzzy supervisors. As a continuation, this paper addresses the reliable decentralized control of FDESs in face of possible failures of some local fuzzy supervisors. Roughly speaking, for an FDES equipped with n local fuzzy supervisors, a decentralized supervisor is called k-reliable (1 ≤ k ≤ n) provided that the control performance will not be degraded even when n - k local fuzzy supervisors fail. A necessary and sufficient condition for the existence of k-reliable decentralized supervisors of FDESs is proposed by introducing the notions of M̃_uc-controllability and k-reliable coobservability of fuzzy language. In particular, a polynomial-time algorithm to test the k-reliable coobservability is developed by a constructive methodology, which indicates that the existence of k-reliable decentralized supervisors of FDESs can be checked with a polynomial complexity.