A Fuzzy Adaptive Zeroing Neural Network with Noise Tolerance for Time-varying Stein Matrix Equation Solving

Zeroing Neural Network (ZNN) are an effective tool for solving time-varying problems in engineering and computing fields. However, the ZNN model fails to achieve stable convergence in the presence of external noise disturbances. The time-varying Stein matrix equation, as a surrogate of the Lyapunov matrix equation, has essential status in practical engineering applications. Therefore, in order to solve the time-varying Stein matrix equation more effectively, a new fuzzy adaptive tolerant-noise zeroing neural network (FATNZNN) is proposed. Different from the traditional zeroing neural network (ZNN) and tolerant-noise zeroing neural network (TNZNN), FATNZNN has obvious superior characteristics of strengthened convergence and robustness. The superiority of FATNZNN comes from the following two aspect. The FATNZNN has the convergence parameter generated by the Takagi-Sugeno fuzzy logic controller (TSFLC) which can be adaptively adjusted according to the steady-state residual. FATNZNN has an integral term that can resist the effects of interference with different noise. In addition, a new nonlinear activation function, exp-sign activation function (ESAF), is constructed and applied to the FATNZNN model to speed up its convergence. A numerical example with multiple simulations verifies the convergence and robust of FATNZNN from different conditions.