Title: Hybrid Karhunen-Loeve/neural modelling for a class of distributed parameter systems

Authors: Chenkun Qi, Han-Xiong Li

Addresses: Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong. ' Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong

Abstract: Distributed parameter systems (DPS) are a class of infinite dimensional systems. However implemental control design requires low-order models. This work will focus on developing a low-order model for a class of quasi-linear parabolic distributed parameter system with unknown linear spatial operator, unknown linear boundary condition as well as unknown non-linearity. The Karhunen-Loeve (KL) Empirical Eigenfunctions (EEFs) are used as basis functions in Galerkin|s method to reduce the Partial Differential Equation (PDE) system to a nonlinear low-order Ordinary Differential Equation (ODE) system. Since the states of the system are not measurable, a recurrent Radial Basis Function (RBF) Neural Network (NN) observer is designed to estimate the states and approximate unknown dynamics simultaneously. Using the estimated states, a hybrid General Regression Neural Network (GRNN) is trained to be a nonlinear offline model, which is suitable for traditional control techniques. The simulations demonstrate the effectiveness of this modeling method.

Keywords: Karhunen-Loeve expansion; Galerkin method; neural observer; neural modelling; distributed parameter systems; DPS; RBF neural networks; control design.

DOI: 10.1504/IJISTA.2008.016363

International Journal of Intelligent Systems Technologies and Applications, 2008 Vol.4 No.1/2, pp.141 - 160

Published online: 22 Dec 2007 *

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