Unknown Resource Reallocation in a Class of Multiagent Systems: A Distributed Approach With Formation Control Perspectives

This article deals with the challenge of a fair and efficient reallocation of resources in a multiagent system (MAS). A novel dynamic control framework is introduced in which the state of each agent evolves according to a distributed control law. This law ensures the allocation of resources according to predefined weights and promotes a fair distribution among the agents. The control strategy is thoroughly analyzed to show that resource allocation remains well-defined, avoids singularities, and ensures consistent performance. Moreover, it is proved that the total resource allocated remains constant, showing that the system can preserve a crucial invariant throughout its evolution. Theoretical results validate the approach and show its adaptability to changing agent states while maintaining the overall resource constraints. A key advantage of the proposed strategy is that the total amount of resources matching the initial distribution remains unknown to the agents. Instead, through emergent behavior resulting from interaction with other agents, each agent uses an appropriate amount of the resource based on its own requirements. This work contributes to an effective control strategy to achieve stable and fair resource allocation in multiagent networks.