Approximation of dynamical time-variant systems by continuous-time recurrent neural networks

This paper studies the approximation ability of continuous-time recurrent neural networks to dynamical time-variant systems. It proves that any finite time trajectory of a given dynamical time-variant system can be approximated by the internal state of a continuous-time recurrent neural network. Given several special forms of dynamical time-variant systems or trajectories, this paper shows that they can all be approximately realized by the internal state of a simple recurrent neural network.