A Varying-Gain Recurrent Neural Network and Its Application to Solving Online Time-Varying Matrix Equation

In mathematics and engineering fields, solving online time-varying matrix equation P(t)X(t)Q(t) = W(t) problem is fundamental and vital. A novel varying-gain recurrent neural network (VG-RNN) is proposed to obtain the online solution of such time-varying matrix equation problem. Distinguished from the conventional gradient-based neural network (termed as GNN), zeroing neural network (termed as ZNN), and finite-time zeroing neural network (termed as FTZNN), the design parameter of VG-RNN is changing with time t goes. Theoretical analysis proves that VG-RNN achieves super-exponential convergent performance when solving the online time-varying matrix equation. Simulation comparisons illustrate that VG-RNN possesses the capability of faster convergence rate than that of GNN, ZNN, and FTZNN. Besides, activated by different activation functions, the convergence performance of VG-RNN can be improved.