A Dynamic Parameter Noise-Tolerant Zeroing Neural Network for Time-Varying Quaternion Matrix Equation With Applications

As a common and significant problem in the field of industrial information, the time-varying quaternion matrix equation (TV-QME) is considered in this article and addressed by an improved zeroing neural network (ZNN) method based on the real representation of the quaternion. In the light of an improved dynamic parameter (IDP) and an innovative activation function (IAF), a dynamic parameter noise-tolerant ZNN (DPNTZNN) model is put forward for solving the TV-QME. The presented IDP with the character of changing with the residual error and the proposed IAF with the remarkable performance can strongly enhance the convergence and robustness of the DPNTZNN model. Therefore, the DPNTZNN model possesses fast predefined-time convergence and superior robustness under different noise environments, which are theoretically analyzed in detail. Besides, the provided simulative experiments verify the advantages of the DPNTZNN model for solving the TV-QME, especially compared with other ZNN models. Finally, the DPNTZNN model is applied to image restoration, which further illustrates the practicality of the DPNTZNN model.