Consensus of Multi-agent System via Constrained Invariant Set of a class of Unstable System

TL;DR

This paper presents a novel method for achieving output consensus in heterogeneous multi-agent systems with input constraints, using a constrained invariant set approach based on the Internal Model Principle for certain unstable systems.

Contribution

It characterizes the maximal constraint admissible invariant set for a class of unstable agent-reference systems, enabling constraint satisfaction in consensus.

Findings

MCAI sets exist for certain unstable systems and can be computed.

The approach successfully achieves output consensus while respecting input constraints.

Examples demonstrate the effectiveness of the proposed method.

Abstract

This work shows an approach to achieve output consensus among heterogeneous agents in a multi-agent environment where each agent is subject to input constraints. The communication among agents is described by a time-varying directed/undirected graph. The approach is based on the well-known Internal Model Principle which uses an unstable reference system. One main contribution of this work is the characterization of the maximal constraint admissible invariant set (MCAI) for the combined agent-reference system. Typically, MCAI sets do not exist for unstable system. This work shows that for an important class of agent-reference system that is unstable, MCAI exists and can be computed. This MCAI set is used in a Reference Governor approach, combined with a projected consensus algorithm, to achieve output consensus of all agents while satisfying constraints of each. Examples are provided to illustrate the approach.