Two novel cold-start multistage neural solvers for constrained nonlinear equations with extended time horizons.

Abstract

To address the linear-constrained system of nonlinear equations (LC-SNEs), a key challenge in industrial applications such as robotics, we introduce the method of cold-start multistage zeroing neural solvers (CM-ZNSs). This method incorporates a cold-start phase along the negative half-axis of the time axis, to pursue long-time duration and minimal dependence on initial conditions. The designed CM-ZNSs are based on zeroing neural dynamics (ZND), which, although effective in solving LC-SNE, are typically short in duration and heavily dependent on initial states due to limitations in mass matrices. We first design five single-stage zeroing neural solvers (SS-ZNSs) to tackle the target LC-SNE. After evaluating the strengths and weaknesses of each SS-ZNS in terms of four performance metrics-time duration, convergence speed, noise tolerance, and calculation accuracy-we divide the solution process into multiple stages, each with distinct priorities. These stages include a cold-start phase aimed at finding a reasonable initial solution, followed by stages focused on improving convergence, accuracy, or noise tolerance. Different ZNDs are strategically employed at each stage. This work proposes the CM-ZNS for the first time and designs two CM-ZNSs specifically for solving LC-SNE. Through rigorous analysis and extensive comparative experiments, we demonstrate that CM-ZNSs outperform SS-ZNSs across all four-evaluation metrics. Additionally, a fuzzy logic-based approach is employed to automatically adjust the cold-start parameter, ensuring the desired time duration for the solution.