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Improved multi-agent controllability processing technique based on equitable partition.

Mengmeng Su1, Zhijian Ji1, Yungang Liu2

  • 1Institute of Complexity Science, College of Automation, Qingdao University, Qingdao, Shandong, 266071, China; Shandong Key Laboratory of Industrial Control Technology, Qingdao, Shandong, 266071, China.

ISA Transactions
|March 19, 2023
PubMed
Summary
This summary is machine-generated.

This study investigates multi-agent system controllability using equitable partition and automorphism. New sufficient conditions are presented, overcoming limitations of previous necessary-condition-only methods for complex network structures.

Keywords:
AutomorphismControllabilityEigenvectorEquitable partitionMulti-agent systems

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Area of Science:

  • Control Theory
  • Network Science
  • Graph Theory

Background:

  • Controllability is crucial for multi-agent systems.
  • Equitable partition and automorphism are advanced graph-theoretic tools.
  • Existing methods for controllability analysis have limitations.

Purpose of the Study:

  • To develop novel conditions for assessing multi-agent system controllability.
  • To utilize equitable partition and automorphism for controllability analysis.
  • To address limitations of solely relying on necessary conditions.

Main Methods:

  • Analysis of connection matrix rank for incompletely connected cells.
  • Eigenvalue and eigenvector analysis of L and Lπ for multi-cell systems.
  • Investigation of quotient graph controllability and leader node influence.

Main Results:

  • A necessary condition for controllability based on connection matrix rank.
  • Sufficient and necessary conditions derived from eigenvalues/eigenvectors.
  • Determination of the lower bound for the controllable subspace.
  • Identification of the gap between necessary and sufficient conditions.

Conclusions:

  • Sufficient conditions for controllability judgments are established using equitable partition and automorphism.
  • This work provides a method to overcome the limitations of equitable partition yielding only necessary conditions.
  • The findings offer enhanced analytical capabilities for complex multi-agent systems.