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LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

Huaguang Zhang, Tao Feng, Hongjing Liang

IEEE Transactions on Neural Networks and Learning Systems

|November 6, 2015

Summary

A new optimal distributed cooperative design method using linear quadratic regulator (LQR) ensures synchronization in multiagent systems. Faster synchronization speeds reduce the effective region, but gain margins enhance performance.

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Area of Science:

Control Theory
Systems Engineering
Networked Systems

Background:

Multiagent systems require robust synchronization control for coordinated behavior.
Existing methods may struggle with model uncertainties or specific network topologies.
Linear quadratic regulator (LQR) offers optimal control but requires adaptation for distributed systems.

Purpose of the Study:

To develop a novel LQR-based optimal distributed cooperative design for synchronization in linear discrete-time multiagent systems.
To establish sufficient conditions for synchronization based on graph eigenvalue properties.
To investigate the trade-off between synchronizing speed and the synchronization region, and to introduce model-free design capabilities.

Main Methods:

A linear quadratic regulator (LQR)-based optimal distributed cooperative control design is formulated.
Sufficient conditions for synchronization are derived using eigenvalue analysis of the fixed, directed graph.
Approximate dynamic programming is integrated to enable model-free cooperative design.
Weighting matrices are optimized by leveraging the guaranteed gain margin of the regulators.

Main Results:

Sufficient conditions for synchronization are established, defining a circular region in the complex plane for graph eigenvalues.
A trade-off is identified: faster synchronization speeds lead to a smaller synchronization region.
The use of gain margins in weighting matrix selection improves synchronizing capacity.
The proposed method is validated through two numerical examples, demonstrating its effectiveness.

Conclusions:

The developed LQR-based method provides an effective framework for distributed cooperative synchronization in linear discrete-time multiagent systems.
The eigenvalue-based conditions offer clear criteria for achieving synchronization.
The integration of approximate dynamic programming extends the method to model-free scenarios, enhancing its practical applicability.