Robust Cooperative Output Regulation of Discrete-Time Heterogeneous Multi-Agent Systems

TL;DR

This paper develops a robust control framework for discrete-time heterogeneous multi-agent systems, providing convex conditions for designing structured control gains that ensure cooperative output regulation despite uncertainties.

Contribution

It introduces a structured Lyapunov inequality and LMIs for global and local control gain design, advancing robust cooperative control of heterogeneous MASs.

Findings

LMI-based conditions guarantee the existence of suitable control gains.

Structured control design can be decoupled into agent-wise problems.

Relationships between global and local control gain sets are characterized.

Abstract

This article considers robust cooperative output regulation of discrete-time uncertain heterogeneous (in dimension) multi-agent systems (MASs). We show that the solvability of this problem with an internal model-based distributed control law reduces to the existence of a structured control gain that makes the nominal closed-loop system matrix of the MAS Schur. Accordingly, this article focuses on global and agent-wise local sufficient conditions for the existence and design of such a structured control gain. Based on a structured Lyapunov inequality, we present a convexification that yields a linear matrix inequality (LMI), whose feasibility is a global sufficient condition for the existence and design. Considering the individual nominal dynamics of each agent, the existence is also ensured if each agent solves a structure-free control problem. Its convexification yields LMIs that allow each agent to separately design its structure-free control gain. Lastly, we study the relationships between the sets of control gains emerging from both global and local perspectives.