Modeling and Optimal Supervisory Control of Networked Discrete-Event Systems and Their Application in Traffic Management

In this paper, we investigate the modeling and control of networked discrete-event systems (DESs), where a supervisor is connected to the plant via an observation channel and the control commands issued by the supervisor are delivered to the actuator of the plant via a control channel. Communication delays exist in both the observation channel and the control channel. First, a novel modeling framework for the supervisory control of DESs subject to observation delays and control delays is presented. The framework explicitly models the interaction process between the plant and the supervisor over the communication channels. Compared with the previous work, a more accurate “dynamics” of the closed-loop system is specified. Under this framework, we further discuss how to estimate the states of the closed-loop system in the presence of observation delays and control delays. Based on the state estimation, we synthesize an optimal supervisor on the fly to maximize the controlled behaviors while preventing the system from leaving the desired behaviors under communication delays. We compare the proposed supervisor with the supervisor proposed in the literature and show that the proposed supervisor is more permissive. As an application, we show how the proposed approach can be applied to manage vehicles in a signal intersection. Finally, we show how to extend the proposed framework to model a system whose actuators and sensors are distributed at different sites.