A Stability-Guarantee Beamforming Scheme in Multi-Loop Wireless Control Systems

In this paper, we propose a stability-guarantee beamforming (BF) scheme for a multi-loop wireless control system, where a multi-antenna controller adopts the receiving BF technique to concurrently manage multiple control loops operating on the same spectrum. Specifically, we first use the convergence rate to characterize the control performance, and combine it with the pre-defined Lyapunov-like function to derive the control stability condition. Then, in order to improve the control performance while preserving the stability, an optimization problem is formulated to minimize the maximum convergence rate among all control loops, subject to the transmit power budget of each control loop and control stability condition. Since the original problem is mathematically complicated, with the help of zero-forcing principle, we propose an iterative algorithm using Lyapunov stability theorem, exponential accumulation and sequential convex approximation to solve it efficiently. Finally, simulation results verify that the introduction of BF in our scheme can significantly improve the control stability and reduce the control cost compared with the existing scheduling-based control scheme.