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Decentralized nondeterministic supervisory control of discrete event systems

This paper studies the decentralized supervisory problem using nondeterministic supervisors. Nondeterministic supervisory control under partial observation was proposed by Kumar et al. (June 2004) by allowing nondeterminism in control policies, which lead to the existence condition of achievability that is weaker than controllability and observability combined and is algebraically better behaved. In this paper, we extend nondeterministic control to the decentralized setting. Using the simple conjunctive rule of decision fusion, we present a definition of co-achievability to characterize the languages which can be achieved through decentralized nondeterministic supervisors. Co-achievability is weaker than controllability and co-observability combined. Other properties of co-achievable languages are presented, and the relationship between achievability and co-achievability is established. We derive necessary and sufficient conditions for target and range control problems. The existence conditions are polynomially verifiable, and also local supervisors can be polynomially synthesized.