Nonlinearly Activated IEZNN Model for Solving Time-Varying Sylvester Equation

Abstract

Zeroing neural network (ZNN) is an effective method to calculate time-varying problems. However, the ZNN and its extensions separately addressed the robustness and the convergence. To simultaneously promote the robustness and finite-time convergence, a nonlinearly activated integrationenhanced ZNN (NIEZNN) model based on a coalescent activation function (C-AF) has been designed for solving the time-varying Sylvester equation in various noise situations. The C-AF with an optimized structure is convenient for simulations and calculations, which promotes NIEZNN accelerates convergence speed without remarkable efficiency loss. The robustness and the finite-time convergence of the NIEZNN model have been proved in theoretical analyses. Further more, the upper bounds of convergence time of the NIEZNN model and the noise-attached NIEZNN model have been deduced in theory. At last, numerical comparative results and the application to mobile manipulator have validated the efficiency and superiority of the NIEZNN model based on the designed coalescent activation function.

Advances on intelligent algorithms for scientific computing: an overview

“…For example, in Jian et al (2020), a class of neural network models was presented for solving the time-varying Sylvester equation, where the authors considered three different types of non-linear activation functions and provided a detailed theoretical derivation to validate the convergence performance of the proposed models. Similarly, Lei et al proposed an integral structured neural network model with a coalescent activation function optimized for the solution of the time-varying Sylvester equation (Lei et al, 2022). For non-convex and non-linear optimization problems, an adaptive parameter convergence-differential neural network (CDNN) model with nonlinear activation functions was proposed in Zhang et al (2018d), and the authors verified the global convergence and robustness of the model by theoretical analysis and numerical experiments.…”

“…LAF (1) Linear (Ding et al, 2014;Zhang et al, 2019;Jian et al, 2020;Xiao et al, 2020c;Dai et al, 2022) PAF (2) Non-linear (Jian et al, 2020) BPAF (3) Non-linear (Zhang et al, 2018a;Lei et al, 2022) PSAF (4) Non-linear (Zhang et al, 2018d) HSAF (5) Non-linear (Xiao et al, 2017b; SBPAF ( 6) Non-linear & Finite-time convergence (Xiao, 2017a(Xiao, , 2019Xiao et al, 2018aXiao et al, , 2019d TSBPAF ( 7) Non-linear & Finite-time convergence (Liao et al, 2022a) (3) Bipolar sigmoid activation function (BPAF):…”

“…Similarly, in Xiang et al (2018a), the authors proposed a discrete Z-type neural network (DZTNN) model for the same dynamic Lyapunov equation, which exhibited inherent noise tolerance and exact solution attainment under various types of noise. Additionally, various neural network models (Xiao, 2017b;Xiao and He, 2021;Lei et al, 2022;Han et al, 2023) have been put forward for solving the time-varying Sylvester equations H(t)J(t) − J(t)H(t) = −K(t).…”