A Learning-based Synthesis Approach to Decentralized Supervisory Control of Discrete Event Systems with Unknown Plants

In this paper, we consider the problem of automatic synthesis of decentralized supervisor synthesis for uncertain discrete event systems. In particular, we study the case when the uncontrolled plant is unknown a priori. To deal with the unknown plants, we first characterize the co-normality of prefixclosed regular languages and propose formulas for computing the supremal co-normal sublanguages; then sufficient conditions for the existence of decentralized supervisors are given in terms of language controllability and co-normality and a learning-based algorithm to synthesize the supervisor automatically is proposed. Moreover, the paper also studies the on-line decentralized supervisory control of concurrent discrete event systems that are composed of multiple interacting unknown modules. We use the concept of modular controllability to characterize the necessary and sufficient conditions for the existence of the local supervisors, which consist of a set of local supervisor modules, one for each plant module and which determines its control actions based on the locally observed behaviors, and an on-line learning-based local synthesis algorithm is also presented. The correctness and convergence of the proposed algorithms are proved, and their implementation are illustrated through examples.