Robust Beamforming for Communication and Control Co-Design in Multi-Loop Wireless Control System

In this letter, a robust transmit scheme is proposed to facilitate the co-design of communication and control in multi-loop wireless control systems (WCS), where the controller equipped with multi-antenna adopts beamforming (BF) technology to suppress various interference and improve link reliability simultaneously. To this end, we first establish an optimization problem to minimize the weighted sum of control cost deviation and energy consumption, while satisfying the control stability of each loop and the constraints of transmit power budget and internetwork interference level. Since the original problem is non-convex, we then convert the control stability constraint into a probabilistic constraint form with the lower bound probability of successful transmission. Furthermore, by jointly using the Bernstein Inequalities and successive convex approximation approach, we propose a robust BF scheme to implement communication and control co-design for multi-loop control system. Finally, simulation results demonstrate that our proposed method can significantly reduce the total system cost while maintaining the control stability and the interference power less than the acceptable level.