Hybrid Karhunen-Loeve/neural modelling for a class of distributed parameter systems. (14th January 2008)

• Record Type: Journal Article
• Authors: Qi, Chenkun; Li, Han-Xiong
• Is Part Of: International journal of intelligent systems technologies and applications. Volume 4:Number 1/2(2008)
• Page Start: 141
• Page End: 160
• Publication Date: 2008-01-14
• Subjects: Karhunen-Loeve expansion -- Galerkin method -- neural observer -- neural modelling -- distributed parameter systems -- DPS -- RBF neural networks -- control design; Artificial intelligence -- Periodicals; Intelligent control systems -- Periodicals; 006.3
• Languages: English
• ISSNs: 1740-8865

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.