# Low-rank LQR Optimal Control Design over Wireless Communication Networks

arXiv: https://arxiv.org/abs/2301.13729 · HTML: https://mlsanity.com/paper/2301.13729/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)

## Abstract (arXiv)

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.