Research on the Consensus Convergence Rate of Multi-Agent Systems Based on Hermitian Kirchhoff Index Measurement

Area of Science:

• Control Theory
• Network Science
• Complex Systems

Background:

• Multi-agent systems (MAS) often use simple graph topologies (directed/undirected) to analyze consensus convergence.
• Increasing system complexity necessitates more sophisticated network models to capture interaction heterogeneity.
• Existing models may not fully represent the nuanced interactions in advanced MAS.

Purpose of the Study:

• To investigate strategies for enhancing consensus convergence rates in MAS.
• To introduce hybrid networks as a more comprehensive interaction topology.
• To propose and validate a novel metric for quantifying convergence.

Main Methods:

• Utilizing hybrid networks to model agent interactions.
• Proposing the Hermitian Kirchhoff index, a novel metric based on resistance distance.
• Applying first-order eigenvalue perturbation analysis to study network modifications.
• Conducting numerical simulations to validate theoretical results.

Main Results:

• The Hermitian Kirchhoff index effectively quantifies consensus convergence rates in MAS with hybrid networks.
• Analysis reveals how adding/removing network edges impacts the Hermitian Kirchhoff index.
• Eigenvalue perturbation theory successfully links network changes to algebraic connectivity.
• Simulations confirm the theoretical predictions and the metric's efficacy.

Conclusions:

• Hybrid networks offer a more robust framework for modeling MAS interactions.
• The Hermitian Kirchhoff index provides a valuable tool for analyzing and optimizing MAS consensus.
• Network topology modifications can be strategically managed to improve convergence rates.