Achieving Optimal Output Consensus for Discrete-time Linear Multi-agent Systems with Disturbance Rejection

TL;DR

This paper develops a distributed control protocol for discrete-time linear multi-agent systems that achieves optimal output consensus despite external disturbances, by integrating an optimal signal generator, disturbance observer, and reference tracking controller.

Contribution

It introduces a novel embedded design combining optimal signal generation, disturbance rejection, and tracking control for high-order multi-agent systems with directed communication.

Findings

The proposed control guarantees output consensus and cost minimization.

The disturbance observer effectively rejects external disturbances.

Numerical example confirms the control law's effectiveness.

Abstract

In this paper, an optimal output consensus problem is studied for discrete-time linear multiagent systems subject to external disturbances. Each agent is assigned with a local cost function which is known only to itself. Distributed protocols are to be designed to guarantee an output consensus for these high-order agents and meanwhile minimize the aggregate cost as the sum of these local costs. To overcome the difficulties brought by high-order dynamics and external disturbances, we develop an embedded design and constructively present a distributed rule to solve this problem. The proposed control includes three terms: an optimal signal generator under a directed information graph, an observer-based compensator to reject these disturbances, and a reference tracking controller for these linear agents. It is shown to solve the formulated problem with some mild assumptions. A numerical example is also provided to illustrate the effectiveness of our proposed distributed control laws.