Dynamic recurrent neural networks for approximation of nonlinear systems

Abstract The approximation capability of a class of continuous-time dynamic recurrent neural networks (DRNNs) described by a set of parameterized differential equations with multi-inputs and multi-outputs (MIMO) is addressed. It is proved that the outputs of such a DRNN with an appropriate initial state may be used to approximate uniformly the output trajectories of a given MIMO nonlinear system over finite-time intervals fot every continuous and bounded input signal. It is also shown that some states of the DRNN are capable of approximating uniformly a state space trajectory produced by either a continuous-time nonlinear system or a continuous function on a finite-time interval