This paper considers a LQR optimal control design problem for distributed control systems with multi-agents. To control large-scale distributed systems such as smart-grid and multi-agent robotic systems over wireless communication networks, it is desired to design a feedback controller by considering various constraints on communication such as limited power, limited energy, or limited communication bandwidth, etc. In this paper, we focus on the reduction of communication energy in an LQR optimal control design problem on wireless communication networks. By considering the characteristic of wireless communication, i.e., Radio Frequency (RF) signal can spread in all directions in a broadcast way, we formulate a low-rank LQR optimal control model to reduce the communication energy in the distributed feedback control system. To solve the problem, we propose an Alternating Direction Method of Multipliers (ADMM) based algorithm. Through various 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 focuses on reducing the number of communication links in a network, in terms of energy consumption, system stability margin against noise and error in communication.

翻译：本文研究了多智能体分布式控制系统的LQR最优控制设计问题。针对智能电网和多智能体机器人系统等大规模分布式系统在无线通信网络上的控制需求，需要综合考虑通信功率、能量或带宽等约束条件来设计反馈控制器。本文聚焦于降低无线通信网络中LQR最优控制设计问题的通信能量消耗。通过利用无线通信的特性——射频信号以广播方式全向传播——建立了低秩LQR最优控制模型以降低分布式反馈控制系统中的通信能量。为解决该问题，我们提出了一种基于交替方向乘子法的算法。通过大量数值实验证明，与以往关注减少网络中通信链路数量的稀疏LQR最优控制设计相比，采用低秩结构设计的反馈控制器在能耗、系统抗噪声稳定性及通信误差鲁棒性方面均表现更优。