A disturbance suppression second-order penalty-like neurodynamic approach to distributed optimal allocation

This paper proposes an efficient penalty-like neurodynamic approach modeled as a second-order multi-agent system under external disturbances to investigate the distributed optimal allocation problems. The sliding mode control technology is integrated into the neurodynamic approach for suppressing the influence of the unknown external disturbance on the system’s stability within a fixed time. Then, based on a finite-time tracking technique, resource allocation constraints are handled by using a penalty parameter approach, and their global information is processed in a distributed manner via a multi-agent system. Compared with the existing neurodynamic approaches developed based on the projection theory, the proposed neurodynamic approach utilizes the penalty method and tracking technique to avoid introducing projection operators. Additionally, the convergence of the proposed neurodynamic approach is proven, and an optimal solution to the distributed optimal allocation problem is obtained. Finally, the main results are validated through a numerical simulation involving a power dispatch problem.