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Modelling and Adaptive Filtering of Nonlinear Systems Using Neural Network

For some classes of nonlinear systems or time series, an operating point dependent ARMA model can be used to represent the system. In this paper we use the neural networks to identify such a model which can then be converted to its equivalent statespace re

Modelling and Adaptive Filtering of Nonlinear Systems Using Neural Network Zhi Qiao Wu and Chris J. Harris

Image, Speech and Intelligent System Research Group Department of Electronics and Computer Science University of Southampton, Southampton SO17 1BJ, UK Email: zqw@ecs.soton.ac.uk http://www-isis.ecs.soton.ac.uk Technical Report: c University of Southampton

For some classes of nonlinear systems or time series, an operating point dependent ARMA model can be used to represent the system. In this paper we use the neural networks to identify such a model which can then be converted to its equivalent statespace representation. Using this state-space form, a Kalman lter can be applied to estimate the state, and a simulated example is given. Keywords: Nonlinear System, System Identi cation, State Estimation, Kalman Filter.

Abstract

1 Introduction The general form of a discrete-time, single-input, single-output (SISO) stochastic nonlinear system can be given by:

y(t)= f (y(t? 1);:::; y(t? n); u(t? d? 1);:::; u(t? d? m))+ !(t);

(1)

where f (:) is an unknown nonlinear function, u(t) and y(t) are the measured input and output of the system respectively, and m; n and d are known a priori and represent the orders and time-delays of the model, f!(t)g denotes a white noise sequence. For some classes of nonlinear systems, if a linear model at a xed operating point is used for a local system representation, a global system representation can be realised via a composite set of linear models which correspond to the di erent operating points (the total number of linear models may be nite or in nite). It is therefore possible to express certain global nonlinear systems as a set of linear systems whose parameters are unknown nonlinear functions of its measurable operating points. In this case, the non-linear system in a general model (1) can then be expressed as:

y(t)= a (Ot )y(t? 1)++ an(Ot)y(t? n)+b (Ot)u(t? d? 1)++ bm (Ot)u(t? d? m)+ !(t); 1 1

(2)

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