Reliable decentralized supervisory control of discrete event systems with marked language specifications

We consider a discrete event system controlled by a decentralized supervisor consisting of n local supervisors. In our previous work, we studied reliable decentralized supervisory control for closed language specifications. We extend this work to the specifications given by marked languages. A decentralized supervisor is said to be k-reliable (1⩽k⩽n) if it exactly achieves a specification language without blocking 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. We present necessary and sufficient conditions for the existence of a k-reliable decentralized supervisor. Then we define a weaker version of k-reliability, called weak k-reliability, by relaxing the nonblocking requirement. We obtain necessary and sufficient conditions for the existence of a weakly k-reliable decentralized supervisor. Moreover, we propose an iterative scheme for computing a sublanguage of a specification for which the existence conditions of a weakly k-reliable decentralized supervisor are satisfied