An intelligent fuzzy robustness ZNN model with fixed‐time convergence for time‐variant Stein matrix equation. Issue 12 (5th September 2022) - Dai, Jianhua; Luo, Liu; Xiao, Lin; Jia, Lei; Li, Xiaopeng
Abstract: On account of the rapid progress of zeroing neural network (ZNN) and the extensive use of fuzzy logic system (FLS), this article proposes an intelligent fuzzy robustness ZNN (IFR‐ZNN) model and applies it to solving the time‐variant Stein matrix equation (TVSME) problem. Be different from ZNN models before, the IFR‐ZNN model uses a fuzzy parameter as the design parameter and adopts a first proposed improved nonlinear piecewise activation function. Particularly, the FLS that generates the fuzzy parameter utilizes an improved membership function of nonuniform distribution which can improve the adaptability and robustness of the IFR‐ZNN model. Based on the above two optimizations, the proposed IFR‐ZNN model possesses three significant advantages: (1) fixed‐time convergence independent of initial states; (2) superior robustness to tolerate two kinds of noises simultaneously; and (3) better adaptiveness based on computational error. Besides, the upper bounds of fixed‐time convergence of the IFR‐ZNN model under noisy or non‐noisy situations are calculated theoretically, and the stability as well as the excellent adaptability are analyzed in detail. Finally, simulation comparison results manifest the availability and meliority of the proposed IFR‐ZNN model in solving the TVSME problem.