On hyperbolic sine activation functions used in ZNN for time-varying matrix square roots finding

A special class of recurrent neural network (RNN) termed Zhang neural network (ZNN) has recently been proposed for time-varying matrix square roots finding. Such a ZNN model can be constructed via monotonically-increasing odd activation functions to obtain the theoretical time-varying matrix square roots in an error-free manner. Different choices of activation functions lead to different performance of the ZNN model. In this paper, to pursue the superior convergence and robustness, a special type of activation functions (i.e., hyperbolic sine activation functions) is used in the ZNN model for online solution of time-varying matrix square roots. Theoretical analysis and simulation results further demonstrate the superior performance of the ZNN model using hyperbolic sine activation functions in the context of (very) large model-implementation errors, in comparison with that using linear activation functions.