Reliable decentralized supervisory control of discrete event systems

We consider a discrete event system controlled by a decentralized supervisor consisting of n local supervisors, and formulate a new decentralized supervisory control problem, called a reliable decentralized supervisory control problem. A decentralized supervisor is said to be k-reliable (1 less than or equal to k less than or equal to n) if it exactly achieves a specification language under possible failures of any less than or equal to n - k local supervisors. So, k denotes the minimal number of local supervisors required to achieve the specification. First, we present necessary and sufficient conditions for the existence of a k-reliable decentralized supervisor. Next, we consider the case that a L-reliable decentralized supervisor for a given specification language does not exist. We take two approaches in this case. In the first approach, we present an algorithm for computing a sublanguage of the specification that satisfies the existence conditions of a k-reliable decentralized supervisor. In the second one, we use a coordinator to synthesize a k-reliable decentralized supervisor without altering the specification.