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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.
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.
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