Linear Quadratic Regulator Design for Multi-input Systems with A Distributed Cooperative Strategy

TL;DR

This paper introduces a novel distributed cooperative LQR controller for multi-input systems, enabling agents to control the system with minimal communication while ensuring stability and performance.

Contribution

It proposes a fully distributed cooperative LQR controller that requires only local communication and joint controllability, reducing communication overhead and improving control performance.

Findings

Guaranteed boundedness and convergence of controller gains.

Achieved better trade-off between control performance and communication cost.

Validated effectiveness through numerical examples.

Abstract

In this paper, a cooperative Linear Quadratic Regulator (LQR) problem is investigated for multi-input systems, where each input is generated by an agent in a network. The input matrices are different and locally possessed by the corresponding agents respectively, which can be regarded as different ways for agents to control the multi-input system. By embedding a fully distributed information fusion strategy, a novel cooperative LQR-based controller is proposed. Each agent only needs to communicate with its neighbors, rather than sharing information globally in a network. Moreover, only the joint controllability is required, which allows the multi-input system to be uncontrollable for every single agent or even all its neighbors. In particular, only one-time information exchange is necessary at every control step, which significantly reduces the communication consumption. It is proved that the boundedness (convergence) of the controller gains is guaranteed for time-varying (time-invariant) systems. Furthermore, the control performance of the entire system is ensured. Generally, the proposed controller achieves a better trade-off between the control performance and the communication overhead, compared with the existing centralized/decentralized/consensus-based LQR controllers. Finally, the effectiveness of the theoretical results is illustrated by several comparative numerical examples.