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Online Supervisory Control of Networked Discrete Event Systems With Control Delays

We investigate state estimation and safe controller synthesis for networked discrete-event systems (DESs), where supervisors send control decisions to plants via communication channels subject to communication delays. Previous works on state estimation of networked DES are based on the open-loop system without utilizing the knowledge of the control policy. In this article, we propose a new approach for online estimation and control of networked DES with control delays. We first propose a new state estimation algorithm for the closed-loop system utilizing the information of control decision history. The proposed state estimation algorithm can be implemented recursively upon the occurrence of each new observable event. Then we investigate how to predict the effect of control delays in order to calculate a control decision online at each instant. We show that the proposed online supervisor can be updated effectively and the resulting closed-loop behavior is safe. Furthermore, we compare the proposed online supervisor with the predictive supervisor proposed in the literature and show that our proposed online supervisor is more permissive than predictive supervisor in the sense of language inclusion.