Simulation and Comparison of Zhang Neural Network and Gradient Neural Network Solving for Time-Varying Matrix Square Roots

A special kind of recurrent neural networks (RNN) has recently been proposed by Zhang et al for online time- varying problems solving. Different from conventional gradient neural networks (GNN), such RNN (or termed specifically as Zhang neural networks, ZNN) are designed based on matrix-valued error functions, instead of scalar-valued error functions. In addition, they are usually depicted in implicit dynamics rather than explicit dynamics. In this paper, we develop, generalize, simulate and compare the ZNN and GNN models for online solution of time-varying matrix square roots. Besides, important simulation techniques are investigated to help simulate both models. Computer-simulation results via power-sigmoid activation functions further substantiate the superior ZNN convergence in time-varying problems solving as compared to the GNN model.