Reliable supervisory control for general architecture of decentralized discrete event systems

In this paper, we investigate the reliable decentralized supervisory control of discrete event systems (DESs) under the general architecture, where the decision for controllable events is a combination of the conjunctive and disjunctive fusion rules. By reliable control, we mean that the performance of closed-loop systems will not be degraded even in the face of possible failures of some local supervisors. The main contributions are twofold. First, a necessary and sufficient condition for the existence of a kk-reliable decentralized supervisor under the general architecture is presented after introducing notions of Σ˜uc-controllability and kk-reliable Σ˜c-coobservability. Second, a polynomial-time algorithm to verify the reliable Σ˜c-coobservability of a specification is proposed.