Approximation of discrete-time state-space trajectories using dynamic recurrent neural networks

In this note, the approximation capability of a class of discrete-time dynamic recurrent neural networks (DRNN´s) is studied. Analytical results presented show that some of the states of such a DRNN described by a set of difference equations may be used to approximate uniformly a state-space trajectory produced by either a discrete-time nonlinear system or a continuous function on a closed discrete-time interval. This approximation process, however, has to be carried out by an adaptive learning process. This capability provides the potential for applications such as identification and adaptive control