Characteristics-Capturing Neural Dynamics for Solving Time-Dependent Nonlinear Equations With Periodic Noise

Abstract

Nowadays, many dynamic systems show the characteristics of multiple-input-multiple-output and nonlinearity, which usually involve the solution of time-dependent nonlinear equations. This paper focuses on the accurate solution of time-dependent nonlinear equations with periodic noises considered. In the hardware or numerical implementations of an actual system, inevitable internal disturbances or external factors caused by the changeable scene may greatly affect the accuracy of the solution. Most of the existing time-dependent anti-noise neural dynamics (ND) models can effectively suppress some constant noise, but they are not satisfactory when facing some periodic noise with high frequency. To solve this problem, a characteristics-capturing ND (CCND) model is designed, which considers the periodic noise from the perspective of harmonic expansion so as to effectively capture harmonic characteristics and eliminate them. Theoretical analysis proves the robustness of the CCND model with periodic noise disturbance considered. Moreover, numerical simulations and robotic experiments further confirm the effectiveness of the CCND model.