Distributed Linear Quadratic Tracking Control for Leader-Follower Multi-Agent Systems: A Suboptimality Approach

TL;DR

This paper develops a distributed control approach for leader-follower multi-agent systems to achieve tracking consensus with suboptimal cost, extending previous leaderless control results and involving Riccati inequality solutions.

Contribution

It introduces a centralized method for designing suboptimal distributed control laws for leader-follower systems using Riccati inequalities, expanding on prior leaderless control frameworks.

Findings

Control laws ensure tracking consensus in multi-agent systems.

The method guarantees the cost is below a specified threshold.

Simulation demonstrates effectiveness of the proposed approach.

Abstract

In this paper, we extend the results from Jiao et al. (2019) on distributed linear quadratic control for leaderless multi-agent systems to the case of distributed linear quadratic tracking control for leader-follower multi-agent systems. Given one autonomous leader and a number of homogeneous followers, we introduce an associated global quadratic cost functional. We assume that the leader shares its state information with at least one of the followers and the communication between the followers is represented by a connected simple undirected graph. Our objective is to design distributed control laws such that the controlled network reaches tracking consensus and, moreover, the associated cost is smaller than a given tolerance for all initial states bounded in norm by a given radius. We establish a centralized design method for computing such suboptimal control laws, involving the solution of a single Riccati inequality of dimension equal to the dimension of the local agent dynamics, and the smallest and the largest eigenvalue of a given positive definite matrix involving the underlying graph. The proposed design method is illustrated by a simulation example.