Design and analysis of robust nonlinear neural dynamics for solving dynamic nonlinear equation within finite time

Abstract

Dynamic nonlinear equation is a kind of important nonlinear systems, and many practical problems can be formulated as a dynamic nonlinear equation in mathematics to be solved. Inspired by the negative impact of additive noises on zeroing neural dynamics (ZND) for dynamic nonlinear equation, a robust nonlinear neural dynamics (RNND) is designed and presented to achieve noise suppression and finite-time convergence simultaneously. Compared to the existing ZND model only with finite-time convergence, the proposed RNND model inherently possesses the extra robustness property in front of additive noises, in addition to finite-time convergence. Furthermore, design process, theoretical analysis, and numerical verification of the proposed RNND model are supplied in details. Both theoretical and numerical results validate the better property of the proposed RNND model for solving such a nonlinear equation in the presence of external disturbances, as compared to the ZND model.