Chaos Identification of Nonlinear Vibrating System Using Neural Networks and Its Application.

Abstract

This research is concerned with an application of chaos to the identification method of a nonlinear dynamical system using neural networks. In conventional control theory, it is difficult to identify a mathematical model of practical system because of system complexity and the existence of nonlinearity. Instead of theoretical methods, neural networks with different architectures have been applied to the identification and control of a wide class of nonlinear systems. In this paper, we propose a learning control scheme to realize the identification and control of a chaos system, using multilayered neural networks, in which the control performance is satisfied for an unknown controlled object by repeated trials. First, the effectiveness of neural networks is shown in the identification problem of Duffing's chaotic time series data and the possibility of short-term predictability in chaotic system is discussed. Second, a new control technique is proposed which identifies nonlinear systems as nonlinear mapping in the forward direction and employs its inverse mapping as a controller. As a result, it is shown that the network dientified by chaotic time series data is applicable to the prediction and control problem.