Optimal Cross-Layer Design of Sampling Rate Adaptation and Network Scheduling for Wireless Networked Control Systems

Wireless Networked Control Systems (NCS) are increasingly deployed to monitor and control Cyber-Physical Systems (CPS). To achieve and maintain a desirable level of performance, NCS face significant challenges posed by the scarce wireless resource and network dynamics. In this paper, we consider NCS consisting of multiple physical plant and digital controller pairs communicating over a multi-hop wireless network. The control objective is that the plants follow the reference trajectories provided by the controllers. This paper presents a novel optimization formulation for minimizing the tracking error due to (1) discretization and (2) packet delay and loss. The optimization problem maximizes a utility function that characterizes the relationship between the sampling rate and the capability of disturbance rejection of the control system. The constraints come from the wireless network capacity and the delay requirement of the control system. The solution leads to a joint design of sampling rate adaptation and network scheduling, which can be naturally deployed over existing networking systems which have a layered architecture. Based on a passivity-based control framework, we show that the proposed cross-layer design can achieve both stability and performance optimality. Simulation studies conducted in an integrated simulation environment consisting of Matlab/Simulink and ns-2 demonstrate that our algorithm is able to provide agile and stable sampling rate adaptation and achieve optimal NCS performance.