Abstract

Zhang neural network (ZNN) has been proposed since 2001 for various time-varying problems solving, and in this paper its nine novelties differing from the conventional gradient neural network (GNN) are summarized. Then, for solving online the linear matrix equation AXB=C with time-varying coefficients, a ZNN model is revisited as an example. Computer simulations have shown that the ZNN model globally exponentially converges to the theoretical time-varying solution (i. e., Zhang quotient) of such a timevarying linear matrix equation, whereas a GNN model could only approximately approach the solution instead of converging to it exactly. In this paper, the relatively complete theoretical analyses (i. e., theorems and proofs) are presented for such a ZNN model, explaining successfully the ZNN effectiveness and efficiency when solving online time-varying problems (e. g., time-varying linear matrix equation AXB=C), especially using power-sigmoid activation functions.

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