Demand-Driven and Energy-Efficient Transmission for Multi-Loop Wireless Control Systems

This paper considers the multi-loop wireless control system (WCS), where control command is delivered from the remote controller to multiple actuators over shared wireless channels. However, different system dynamics of multiple loops make each loop usually have different demands on the success probability of receiving control commands. Thus, the control performance of overall system is affected by both the transmission reliability and the dynamics of each loop. In this paper, we propose a demand-driven and energy-efficient transmission strategy to adaptive to wireless channels and system dynamics. In order to improve the control performance without burdening the scarce spectrum resources, the remote controller is equipped with multiple antennas, and the transmit beamforming design with power control is adopted to improve the success probability of control commands. In particular, we firstly characterize the control performance of each loop with a pre-defined Lyapunov function, which would decrease exponentially in expectation if the packet loss rate meets the stability condition of each loop. Then, a control stability constrained optimization problem is formulated to minimize the overall cost including energy consumption and linear quadratic Gaussian control cost. The non-trivial probabilistic constraint is effectively handled with the differential accumulation and difference-convex methods. Finally, simulation results verify that the proposed strategy has superiority on reducing control cost and energy consumption without considerations of system dynamics or joint design of transmit beamforming and power control.