Reliable decentralized supervisory control of discrete event systems with communication delays

The reliable decentralized supervisory control of discrete event systems (DESs) with communication delays is investigated in this paper. For a system equipped with n local supervisors, we formalize the notion of k-reliable (1 les k les n) decentralized supervisor under communication delays, in which some local supervisors are allowed to fail and the system can achieve exactly the specification under any k local supervisors. In particular, necessary and sufficient conditions for the existence of a k-reliable decentralized supervisor under communication delays are presented by means of the modified controllability and reliable delay-coobservability. These results can be reduced to those in if the communication delays are negligible. Moreover, the results of can be regarded as a special case of the proposed k-reliable decentralized control with k = n.