Novel Noise-Tolerant Zeroing Neurodynamics Algorithms for Dynamic Nonlinear Least Square Problems With Robot Application

Dynamic nonlinear least square (DNLS) problems are usually encountered in modern engineering, which are challenging to solve due to time-delay errors and noise in practical applications with existing traditional algorithms. This article presents a novel neurodynamics algorithm, termed noise-tolerant zeroing neurodynamics (NTZN), providing a more accurate neurodynamics approach to solve DNLS problems under noisy environments that are pervasive in practical applications. To mitigate computational complexity, the NTZN algorithm integrates optimization techniques such as Broyden–Fletcher–Goldfarb–Shanno (BFGS), Davidon–Fletcher–Powell (DFP), and Dennis–Gay–Welsch (DGW) algorithm for matrix approximation. Theoretical analysis demonstrates that NTZN ensures convergence for both small and large residual conditions, even in the presence of constant or random noise. Experiments including numerical simulations and motion generation application of a UR5 manipulator validate the algorithm’s superior performance and robustness to noise, establishing NTZN algorithm as a robust solution for DNLS problems in practical applications.