Exploiting Chaos in Learning System Identification for Nonlinear State Space Models

The paper presents two learning methods for nonlinear system identification. Both methods employ neural network models for representing state and output functions. The first method of learning nonlinear state space is based on using chaotic or noise signals in the training of state neural network so that the state neural network is designed to produce a sequence in a recursive way under the excitement of the system input. The second method of learning nonlinear state space has an observer neural network devoted to estimate the states as a function of the system inputs and the outputs of the output neural network. This observer neural network is trained to produce a state sequence when the output neural network is forced by the same sequence and then the state neural network is trained to produce the estimated states in a recursive way under the excitement of the system input. The developed identification methods are tested on a set of benchmark plants including a non-autonomous chaotic system, i.e. Duffing oscillator. Both proposed methods are observed much superior than well-known identification methods including nonlinear ARX, nonlinear ARMAX, Hammerstein, Wiener, Hammerstein–Wiener, Elman network, state space models with subspace and prediction error methods.