Reliable decentralized supervisory control of discrete event systems

We consider a discrete event system controlled by a decentralized superviso r consisting of n local supervisors, and formulate a new decentralized supe rvisory control problem, called a reliable decentralized supervisory contro l 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 specificat ion language under possible failures of any less than or equal to n - k loc al supervisors. So, k denotes the minimal number of local supervisors requi red to achieve the specification. First, we present necessary and sufficien t conditions for the existence of a k-reliable decentralized supervisor. Ne xt, we consider the case that a L-reliable decentralized supervisor for a g iven specification language does not exist. We take two approaches in this case. In the first approach, we present an algorithm for computing a sublan guage of the specification that satisfies the existence conditions of a k-r eliable decentralized supervisor. In the second one, we use a coordinator t o synthesize a k-reliable decentralized supervisor without altering the spe cification.