Low-Rank LQR Optimal Control Design for Controlling Distributed Multi-Agent Systems

This paper addresses the problem of optimal control design for distributed control systems with multiple agents, using a Linear Quadratic Regulator (LQR) approach. To effectively control large-scale distributed systems, such as smart-grid and multi-agent robotic systems, it is crucial to design feedback controllers that take into account the various communication constraints, such as limited power, limited energy, or limited communication bandwidth. In this work, we focus on reducing the communication energy in LQR optimal control design on wireless communication networks. Since the Radio Frequency (RF) signal can spread in all directions in a broadcast way, we take advantage of this characteristic to formulate a low-rank LQR optimal control model that can significantly reduce communication energy in distributed feedback control systems. To solve the problem, we propose an algorithm based on the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that a feedback controller designed using low-rank structure can outperform the previous work on sparse LQR optimal control design, which only focused on reducing the number of communication links in a network, in terms of energy consumption.