Analysis of Nonlinear System Dynamics in State Space Modeling with Recurrent Neural Networks

The system identification/modelling problem looks for a suitably parameterized model, representing a given process. The parameters of the model are adjusted to optimize a suitable performance function based on the error between a given process output and identified model's output. The linear system identification field is well established with many classical approaches whereas most of those methods cannot be applied for nonlinear systems [1][7].The problem becomes tougher if the system is completely unknown with only the output time series is available. It has been reported that the capability of Artificial Neural Network to approximate all linear and nonlinear input-output maps makes it predominantly suitable for the identification of nonlinear systems, where only the output time series is available. [1][2][4][5].The work reported here is an attempt to model certain nonlinear systems using recurrent neural networks and asses the model performance and system dynamics using the Lyapunov exponents.