Identifying chaotic systems via a Wiener-type cascade model

In this article we first show a theory that a Wiener-type cascade dynamical model, in which a simple linear plant is used as the dynamic subsystem and a three-layer feed-forward artificial neural network is employed as the nonlinear static subsystem, can uniformly approximate a continuous trajectory of a general nonlinear dynamical system with arbitrarily high precision on a compact time domain. We then report some successful simulation results, by training the neural network using a model-reference adaptive control method, for identification of continuous-time and discrete-time chaotic systems, including the typical Duffing, Henon, and Lozi systems. This Wiener-type cascade structure is believed to have great potential for chaotic dynamics identification, control and synchronization.