Approximation Capability of Continuous Time Recurrent Neural Networks for Non-autonomous Dynamical Systems

Abstract

The main goal of this study is to elucidate the theoretical capability of the continuous time recurrent neural network. In this paper, we show that the approximation capability of the continuous time recurrent network can be extended to non-autonomous dynamical systems with external inputs. Moreover, if the dynamical system has an asymptotically stable periodic solution for a periodic external input, it is shown that the approximation can be extended to the global time interval.