Distributed Resource Allocation for Heterogeneous Linear MASs Over Weight-Unbalanced Digraphs: An Adaptive Weighted Approach

This paper introduces a new distributed control law with adaptive edge weights to address the resource allocation problem (RAP) for heterogeneous linear multi-agent systems (MASs). Unlike most existing works, the communication graph among the agents is assumed to be weight-unbalance and strongly connected, without further constraints, and the actual out-degree information is not accessible. Under assumptions regarding the local cost functions and the communication graph, sufficient conditions for the exponential convergence are derived, ensuring that the agents' outputs converge to the optimal solution to the RAP. Finally, The effectiveness of the proposed control law is demonstrated through an application to a smart grid system.