Optimized Over-the-Air Computation for Wireless Control Systems

The over-the-air controller was recently proposed to enable efficient computation of the control signal for control systems, by leveraging the over-the-air computation concept. This paper introduces a transmit power allocation scheme for the over-the-air controller, where the wireless channel directly produces the control gain of a discrete-time linear control system. The proposed design scheme essentially minimizes the worst effect of the channel noise to the desired control system output, subject to the transmit power limit over the wireless channel. Despite the non-convexity of the problem, we derive the control cost criterion as linear matrix inequalities with transmit power constraints. We comprehensively investigate the control performance and the transmit power cost of the proposed scheme in various scenarios. The proposed optimization scheme shows significant control performance gain against the state-of-the-art solution, while having a comparable transmit power consumption.