A new design formula exploited for accelerating Zhang neural network and its application to time-varying matrix inversion.

Online solution to time-varying matrix inverse is further investigated by proposing a new design formula, which can accelerate Zhang neural network (ZNN) to finite-time convergence. Compared with the existing recurrent neural networks e.g., the gradient neural networks (GNN), and the original Zhang neural network, the proposed neural network (termed finite-time ZNN, FTZNN) makes a breakthrough in the convergence performance (i.e., from infinite time to finite time). In addition, different from the previous processing method (i.e., choosing a better nonlinear activation to accelerate convergence speed), this paper subtly proposes a new design formula to accelerate the original ZNN model and design the new FTZNN model. Besides, theoretical analyses of the design formula and the FTZNN model are given in detail. Simulative results substantiate the effectiveness and superiorness of the proposed FTZNN model for online time-varying matrix inversion, as compared with the GNN model and the original ZNN model.