Finite-Time Consensus Neurodynamic Optimization for Distributed Pseudoconvex Problems with Engineering Applications to Economic Dispatch

This paper proposes an adaptive single-layer distributed neurodynamic optimization approach with the penalty method to address a non-smooth pseudoconvex optimization problem with affine equality and inequality constraints in multi-agent systems, where the global objective function for the agents is pseudoconvex but not required to be differentiable. The target of this approach is to optimize the global objective while ensuring compliance with various constraints. The approach avoids the use of additional auxiliary variables, thereby reducing communication bandwidth and computational complexity. Under mild assumptions, the solution of the designed model is bounded for any initial conditions, to enter their respective feasible domains in finite time, and remain within these domains indefinitely. To achieve finite-time consensus in undirected, connected networks for multi-agent systems, a novel consensus mechanism is introduced to ensure that all agents synchronize their states within finite time. By exploiting the unique pseudoconvexity of the global objective function, the solution trajectory converges to the optimal state of the original problem. Furthermore, the effectiveness of the proposed approach is verified through two simulation experiments, and comparisons with four existing algorithms are conducted to demonstrate its superiority in convergence performance. Finally, an economic dispatch problem in power systems is provided as an engineering application to illustrate the practical applicability of the proposed algorithm.