Low-rank LQR Optimal Control Design over Wireless Communication Networks

TL;DR

This paper introduces a low-rank LQR control design for multi-agent systems over wireless networks, aiming to reduce communication energy while maintaining system stability and performance.

Contribution

It formulates a low-rank control model considering wireless broadcast characteristics and proposes an ADMM-based algorithm for efficient solution, outperforming sparse control methods.

Findings

Reduced communication energy consumption in control systems.

Enhanced system stability margin against noise and communication errors.

Outperforms sparse control methods in numerical experiments.

Abstract

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.