Fixed-Time Distributed Optimization Without Matrix Inversion via Zeroing Neural Networks

Abstract

This paper focuses on the fixed-time distributed optimization problem with time-varying cost functions in multi-agent systems (MASs). For the scenario where all agents share the same Hessian matrix, a control framework for minimizing the global cost function is proposed based on the zero-gradient-sum (ZGS) algorithm. Specifically, integral sliding mode is employed to achieve the initial optimality of local objective functions, thereby satisfying the initial conditions required by the ZGS algorithm. Furthermore, for the case with heterogeneous Hessian matrices among agents, a distributed optimization algorithm integrating distributed gradient estimation and the prediction-correction method (PCM) is designed. Specifically, the distributed gradient estimation enables each agent to reconstruct the global objective gradient information of the system within a fixed time. Both proposed algorithms can achieve fixed-time convergence, and the inverse of the Hessian matrix is approximated online using a zeroing neural network (ZNN), which significantly improves computational efficiency. Finally, numerical simulations are conducted based on the charge balance problem in smart grids to verify the effectiveness and superiority of the proposed algorithms.