A Neurodynamic Approach for Solving Time-Dependent Nonlinear Equation System: A Distributed Optimization Perspective

During industrial smart manufacturing, many problems can be described as a time-dependent nonlinear equation system (TNES) that needs to be solved cooperatively due to large-scale information flows and transmission lines. In this article, a distributed neurodynamic approach is designed for solving a class of TNESs, over multiagent networks from a distributed optimization perspective. To be specific, the TNES is transformed into a distributed time-varying optimization problem (DTOP) to solve. For reformulated DTOP, the proposed neurodynamic approach has ability to jointly drive all agents to reach consensus while optimizing the global objective function. Furthermore, relying on an effective activated function, the finite-time consensus and fixed-time convergence are proved, and the upper bounds of settling time are given as well. This significantly improves the efficiency of the approach in completing practical engineering tasks. Besides, a real-time approximation method is introduced to solve the inverse of the Hessian matrices of the local objective functions in real time, causing the proposed neurodynamic approach to be inverse-free and more suitable for computing complex problems. It is verified that such a real-time approximation method can still ensure convergence within fixed time. Finally, some numerical examples and a case study of multirobot moving target tracking are given to demonstrate the effectiveness of the proposed approach.