ZNN With Fuzzy Adaptive Activation Functions and Its Application to Time-Varying Linear Matrix Equation

In order to improve the effect of the Exp-Sign activation function (ESAF) and the Sinh-Sign activation function (SSAF) on the convergence and robustness of the zeroing neural network (ZNN) model, two fuzzy adaptive activation functions, named FAESAF and FASSAF, are constructed by using a Mamdani fuzzy logic controller (MFLC) in this article. Thus, a novel ZNN with the FAESAF and the FASSAF is proposed to solve the time-varying linear matrix equation. Different from the ESAF and the SSAF, whose parameters are fixed, the newly constructed FAESAF and FASSAF have an adaptive property, which comes from the fact that their parameters are intelligently generated by the MFLC according to the error norm of the ZNN model. In order to highlight the superior predefined time convergence and robustness of the corresponding ZNN model with the FAESAF and the FASSAF, several theorems are provided, and the corresponding proof is given in detail. Furthermore, the ESAF and the SSAF with different values of parameters are used as a comparison in numerical experiments to verify the superior performance of the FAESAF and the FASSAF. From theoretical analysis and numerical results, we can conclude that the ZNN model with the FAESAF and the FASSAF has better predefined time convergence and robustness compared to the ZNN model with the ESAF and the SSAF under the same conditions.