Algebraic connectivity a(G) for various graphs.

Effective communication is crucial for the performance and collaboration within cooperative networked multi-agent systems. However, existing literature lacks comprehensive solutions for dynamically monitoring and adjusting communication topologies to balance connectivity and energy efficiency. This study addresses this gap by proposing a distributed approach for estimating and controlling system connectivity over time. We introduce a modified consensus protocol where agents exchange local assessments of communication link quality, enabling the estimation of a global weighted adjacency matrix without requiring centralized information. The system’s connectivity is measured using the second smallest eigenvalue of the communication graph Laplacian, commonly referred to as algebraic connectivity. Additionally, we enhance the consensus protocol with an adaptive mechanism to expedite convergence, irrespective of system size or structure. Furthermore, we present an analytical method for connectivity control based on the Fiedler vector approximation, facilitating the addition or removal of communication links. This method adjusts control parameters to accommodate minor variations in link quality while reconfiguring the network in response to significant changes. Notably, it identifies and eliminates energy-consuming yet non-contributory links, improving long-term connectivity efficiency. Simulation experiments across diverse scenarios and the number of agents validate the efficacy of our proposed algebraic connectivity estimation and tracking strategy. Results demonstrate robust connectivity maintenance against external disturbances and agent failures, underscoring the practical utility of our approach for real-world multi-agent systems.