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The HoneyComb Paradigm for Research on Collective Human Behavior

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Regional consensus of switched positive multi-agent systems with multiple equilibria.

Junfeng Zhang¹, Pei Zhang², Tarek Raïssi³

¹School of Information and Communication Engineering, Hainan University, Haikou, 570228, China. jfz5678@126.com.

Scientific Reports

|January 18, 2025

Summary

This study develops a new regional consensus protocol for switched positive multi-agent systems, ensuring agent states remain nonnegative and converge to a specific region using an observer-based control strategy.

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Area of Science:

Control Theory
Systems Engineering
Networked Systems

Background:

Multi-agent systems (MAS) are crucial for distributed decision-making.
Achieving consensus in MAS with positive states and multiple equilibria presents significant challenges.
Switched systems introduce further complexity due to dynamic topology and behavior.

Purpose of the Study:

To design a regional proportional-integral-derivative (PID) consensus protocol for switched positive multi-agent systems with multiple equilibria.
To develop an observer-based distributed PID control strategy for enhanced consensus.
To ensure all agent states remain nonnegative and converge within a defined region.

Main Methods:

A novel switched positive consensus error system analyzed using copositive Lyapunov functions.
Construction of a Luenberger observer with multiple equilibria.
Design of the regional consensus protocol using linear programming.

Main Results:

A framework for regional PID consensus in switched positive MAS with multiple equilibria was established.
An effective observer-based distributed PID control protocol was proposed.
Consensus analysis was performed using matrix decomposition, copositive Lyapunov functions, and linear programming.

Conclusions:

The proposed observer-based regional PID consensus protocol effectively drives agent states to a specific nonnegative region.
The methodology provides a robust framework for controlling complex switched positive multi-agent systems.
Numerical examples validated the protocol's efficacy in achieving regional consensus.