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

Area of Science:

• * Computational Mathematics
• * Neural Network Dynamics
• * Robotics and Control Systems

Background:

• * Linear-constrained systems of nonlinear equations (LC-SNEs) are critical in industrial applications like robotics.
• * Existing zeroing neural dynamics (ZND) solvers for LC-SNEs often suffer from short operational durations and sensitivity to initial conditions.
• * Limitations in mass matrices of traditional ZNDs hinder their long-term performance and robustness.

Purpose of the Study:

• * To develop a novel solver method for LC-SNEs that overcomes the limitations of existing approaches.
• * To introduce the cold-start multistage zeroing neural solver (CM-ZNS) for enhanced performance in solving LC-SNEs.
• * To improve the time duration, convergence speed, noise tolerance, and calculation accuracy of neural solvers for LC-SNEs.

Main Methods:

• * Design and implementation of five single-stage zeroing neural solvers (SS-ZNSs) to address the target LC-SNE.
• * Development of the cold-start multistage zeroing neural solver (CM-ZNS) framework, incorporating a cold-start phase for improved initial conditions.
• * Strategic employment of different ZNDs across multiple stages, prioritizing cold-start, convergence, accuracy, and noise tolerance.
• * Utilization of a fuzzy logic-based approach for automatic adjustment of the cold-start parameter to ensure desired solution time duration.

Main Results:

• * CM-ZNSs demonstrate superior performance over SS-ZNSs across all evaluated metrics: time duration, convergence speed, noise tolerance, and calculation accuracy.
• * The cold-start phase effectively establishes a reasonable initial solution, reducing dependence on initial conditions.
• * Rigorous analysis and comparative experiments confirm the enhanced capabilities of the proposed CM-ZNSs.

Conclusions:

• * The proposed CM-ZNS method represents a significant advancement in solving linear-constrained systems of nonlinear equations.
• * CM-ZNSs offer a more robust, accurate, and longer-duration solution compared to traditional single-stage solvers.
• * This work paves the way for more reliable and efficient application of neural solvers in complex industrial problems.