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A special class of recurrent neural network (RNN), termed Zhang neural  network (ZNN) depicted in the implicit dynamics, has recently been proposed  for online solution of time-varying matrix square roots. Such a ZNN model can  be constructed by using monotonically-increasing odd activation functions to  obtain the theoretical time-varying matrix square roots in an error-free  manner. Different choices of activation function arrays may lead to different  performance of the ZNN model. Generally speaking, ZNN model using hyperbolic  sine activation functions may achieve better performance, as compared with  those using other activation functions. In this paper, to pursue the superior  convergence and robustness properties, hyperbolic sine activation functions  are applied to the ZNN model for online solution of time-varying matrix  square roots. Theoretical analysis and computer-simulation results further  demonstrate the superior performance of the ZNN model using hyperbolic sine  activation functions in the context of large model-implementation errors, in  comparison with that using linear activation functions.

Superior performance of using hyperbolic sine activation functions in ZNN illustrated via time-varying matrix square roots finding