RIS-Aided Networked Control Systems: A Goal-Oriented Phase Shift Optimization Approach

In this paper, we present a comprehensive optimization framework for networked control systems, focusing on both communication and control tasks. The system under consideration involves a set of sensors observing the states of multiple physical processes, with the data transmitted over an unreliable wireless channel assisted by a reconfigurable intelligent surface (RIS) with multiple reflecting elements. By considering that the phase shift configuration relies on the statistical channel knowledge, we derive a joint phase shift optimization and control policy that minimizes a performance regulation cost of the system. We characterize the optimal policy and then propose two alternating optimization-based approaches for phase shift design which depend on the system statistics and can therefore be implemented efficiently in practice. We provide a detailed analysis of each approach and show their superiority with respect to other methods.