A Distributed Protocol to Virtualize All-to-All Connectivity in a Class of Multiagent Systems

This article addresses the challenge of achieving virtual full connectivity in multiagent systems (MASs) through a novel distributed protocol. Leveraging finite-time convergent observers, the proposed method enables each agent to estimate the states of all nonneighboring agents, facilitating seamless coordination in scenarios where direct communication links are absent. Unlike conventional approaches that focus on leader-following or partial connectivity frameworks, this method ensures mutual state estimation among all agents, thus enabling scalable control. The proposed model incorporates physical constraints, such as bounded agent velocity, which ensures practical realizability and allows the appropriate tuning of observer parameters to guarantee convergence within a finite time. A smooth transition function is introduced to integrate estimated states into the interaction dynamics, ensuring stability and continuity during the transition to a virtually fully connected topology. The system's properties, including collision avoidance, are preserved throughout this transition by deriving a new potential function that accounts for both directly connected and virtually connected agents. The theoretical contributions are validated through a rigorous analysis of convergence properties and the preservation of key interaction rules. Numerical results demonstrate the applicability of the proposed approach.