A recurrent neural network with predefined-time convergence and improved noise tolerance for dynamic matrix square root finding

Zeroing neural network (ZNN, or termed Zhang neural network after its inventors) is an effective approach to dynamic matrix square root (DMSR) finding arising in numerous fields of science and engineering. The conventional ZNN models can obtain the theoretical DMSR in infinitely long time or in finite time. However, in some applications especially the ones that require to fulfill hard time constraints, these ZNN models may be not competent to guarantee a timely convergence. Hence, for solving DMSR, a ZNN model with explicitly and antecedently definable convergence time is more preferable. Being robust to external noises is very significant for a neural network model. Unfortunately, the existing ZNN models exhibit limited noise-tolerance capability and the corresponding steady-state residual errors would be theoretically bounded when the ZNN models are perturbed by dynamic bounded non-vanishing noises. To enhance the existing ZNN models, by using two novel activation functions, this paper for the first time enables the ZNN model to be predefined-time convergent with improved noise-tolerance capability. The convergence time of the accelerated ZNN model can be explicitly defined as a prior constant parameter. More importantly, such a predefined-time convergent ZNN (PTZNN) is capable of theoretically and completely enduring dynamic bounded vanishing and non-vanishing noises. For handling constant noises such as large constant model-implementation errors, the PTZNN can achieve improved noise-tolerance performance as compared with the existing ZNN models. Comparative simulation results demonstrate that the proposed PTZNN delivers superior convergence and robustness performance for solving DMSR in comparison with the existing ZNN models.