Robust Beamforming for RIS Assisted Wireless Networked Control Systems

The complex electromagnetic environment prevalent in industrial production severely affects the performance of wireless networked control system (WNCS). In this context, we propose a robust beamforming scheme to address this problem, where the controller is equipped with multi-antenna and a reconfigurable intelligent surface (RIS) is deployed to enhance the wireless link quality. With this regard, we first adopt the pre-defined Lyapunov-like function to derive the control stability condition of the production devices. Then, a constrained optimization problem using the concept of communication and control co-design is formulated to minimize the total transmit power while guaranteeing the control stability of WNCS. Assuming that the imperfect channel state information is available, we exploit the fractional programming method to transform the control stability constraint into an outage constraint, and propose an alternative algorithm combining Bernstein inequality with first-order convex approximation to design the active beamformer of the controller and passive beamformer of the RIS. Finally, simulation results demonstrate that compared with the existing methods, our proposed scheme can significantly reduce the power consumption, provided that the control stability is guaranteed.