Abstract
Most of real systems are continuous systems with nonlinearity. Usually, the systems are approximated by linear models, and are analyzed and designed using the well established linear system theory, because the analysis and the design of nonlinear systems are difficult, and the theories for them are not well established. However, there must be an approximation error due to the nonlinearity. In this paper, an approach to identification of nonlinear continuous time systems with measurement noise is proposed. In the approach the parameters of the linear approximate model are estimated from the sampled input-output data of the nonlinear systems by a low-pass filtering method, and the modeling error due to the nonlinearity is compensated by using neural network. Two types of neural network compensators are obtained based on two different ways of approximating the noise removed system output. In the training of the neural network, the teaching signals are provided by data smoothing method which enables on-line noise filtering and thus on-line training. The trained network compensats the modeling error effectively. An illustrative example is given to demonstrate the effectiveness of the proposed approach.
