A nonlinear and noise-tolerant ZNN model solving for time-varying linear matrix equation

The Zhang neural network (ZNN) has attracted a great deal of interest from a large number of researchers because of its significant advantage in solving the various time-varying problems by the monotonously increasing odd activation functions. Many related models have been proposed for time-varying matrix solutions, however, provided that the noise is zero or the preprocessing of de-noising is conducted. Therefore, many of the models previously proposed are not suitable for real-world situations. In this study, a nonlinear and noise-tolerant ZNN model, named NNT-ZNN, is proposed and discussed based on the matrix-valued error function. Theoretically, we prove that the proposed NNT-ZNN model can be globally converged to the theory solution of the considered time-varying equation, regardless of any activation function being applied. In addition, we prove that the resultant NNT-ZNN model has the superior convergence performance beside the existing ZNN models, even when noise is not zero. After that, the simulative results of the resultant NNT-ZNN model are provided by using three illustrative examples to thoroughly validate the correctness of the theoretical analysis. Moreover, the simulation comparison between the proposed NNT-ZNN model and the existing ZNN-1 model is conducted, which further show that availability and excellence of the resultant NNT-ZNN model, and robustness to noise.