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On Scheduling Policy for Multi-process Cyber-Physical System with Edge Computing

In this paper, we consider a cyber-physical system (CPS) with multiple Internet of Things (IoT) devices. There are multiple independent linear time-invariant processes in the system, which are sampled by sensors, scheduled by controllers and controlled by actuators. In the literature of wireless control CPS, commonly assume that the system just have one controller and ignore the processing time on server. In this work we employ the edge computing, the controllers are facilitated by edge server and cloud server. The processing time of status update depends on the characteristic of different processes and servers. By taking into account such conditions, we mainly investigate how to choose the destination of status updates (i.e., edge server or cloud server) to minimize the average Mean Square Error (MSE) of the entire system. To address this issue, we formulate a Markov Decision Process (MDP) problem and obtain the optimal scheduling policy. The threshold property of the optimal scheduling policy is proved, and a suboptimal policy is proposed to overcome the curse of dimensionality. The simulation results illustrate that the selection of controller is related to the timeliness of process and show the superiority of the proposed policies.