Reactive Supervisory Control of Open Discrete-event Systems

Traditional supervisory control theory of discreteevent systems mainly deals with closed systems, and only ensures correct behaviors that can be generated by the system under certain environments that have been captured by the plant model. However, such control methods cannot be applied for many industrial systems nowadays since they are open systems and their behaviors heavily depend on nontrivial interactions with external environments. The key challenge on the control of these open systems is due to the need of the correctness guarantee with respect to all possible environments, which are dynamic, uncertain and sometimes unpredictable. In this paper, we are motivated to extend the conventional DES supervisory control theory to open DESs. Specifically, we consider control objectives that characterize the input-output behaviors of such an open system, and propose a game-theoretic approach to design a reactive supervisor in order to meet the specifications regardless of the external environment behaviors. Necessary and sufficient conditions for the existence of such a reactive supervisor is provided and illustrative examples are given throughout the paper to explain the key definitions and the effectiveness of the proposed game-theoretic supervisor design method.