A varying-gain recurrent neural-network with super exponential convergence rate for solving nonlinear time-varying systems

Abstract

In order to solve a nonlinear time-varying system, a novel varying-gain recurrent neural network (termed as VG-RNN) is proposed and analyzed. To achieve a fast convergent performance, a vector-based unbounded error function is first defined. Second, a varying-gain neural dynamic approach is employed to design the recurrent neural network formula. Being different from the traditional constant-gain recurrent neural networks with fixed design parameters such as the gradient-based neural network (termed as GNN) and the zeroing neural network (termed as ZNN), the gain coefficient of the proposed VG-RNN is time-varying, which can change with time evolves. Otherwise, compared to the previous numerical methods on solving nonlinear time-varying systems, the solution obtained by VG-RNN is more precise. Third, rigorous mathematics analysis proves the super exponential convergence and accuracy of the proposed VG-RNN. Numerical experiments demonstrate the high accuracy, effectiveness and superiority of the VG-RNN compared with the conventional neural networks for solving nonlinear time-varying systems. Furthermore, we hope to apply the theory proposed in this paper to practical nonlinear time-varying automatic control systems, such as robots with nonlinear time-varying systems.