Generalized Second-Order Neurodynamic Approach for Distributed Optimal Allocation

In this article, based on the multiagent system with second-order dynamics, two neurodynamic approaches are proposed to solve the distributed optimal allocation problem (DOAP) with equality resource interaction, inequality resource interaction, and local feasible constraints.over the switching communication topologies. To address the equality and inequality resource interactions in a distributed way, the corresponding auxiliary variables are introduced to ensure the local estimations of Lagrangian multipliers reach consensus in a distributed manner. On this basis, a novel generalized second-order neurodynamic approach is presented to solve the nonsmooth DOAP, and the theoretical proof of convergence is provided. Furthermore, to prevent global information from being involved, another generalized second-order neurodynamic approach is designed and its effectiveness is also analyzed. Finally, a numerical example and an application of the maximum network utility problem are simulated to verify the correctness of the conclusions.