A matching problem between two decoupled multi-agent systems with reference tracking capabilities

Multi-agent systems have emerged as the central framework in which autonomous agents are seamlessly coordinated and co-operate to address complex challenges. The area of matching between multiple swarms has attracted considerable attention, especially in critical domains such as transport, logistics and robotics, where coordination algorithms play an essential role in resource allocation, system performance and overall functionality. This paper addresses the challenges that arise in matching two swarms of agents, addressing issues related to scalability, dynamic environments, and privacy. The proposed solution, based on a theoretical study of emergent behavior in multi-agent systems, revolves around the design of a control law that aims to ensure the convergence of the agents’ positions to a predefined region where the steady-state values remain independent of the agents’ initial conditions. This independence reflects a collective behavior resulting from local interactions between the agents and their engagement with the environment. This property shows that even completely independent swarms can reach a coupled consensus within a predefined region, even in the absence of direct communication. The effectiveness of the proposed approach is supported by numerical simulations and experimental results.