Low-dimensional approximation strategy for a class of nonlinear distributed parameter systems

Abstract

A new low-dimensional approximation strategy is proposed for a class of nonlinear distributed parameter systems (DPS) with nonlinear uncertainties. Firstly, spectral method is used to obtain spectral based model with nominal nonlinear terms of DPS. After neglecting the nonlinear terms of the spectral based model, balanced truncation model reduction is carried out to obtain a balanced transform matrix and reduced linear terms. Lastly, a low-dimensional hybrid intelligent neural network model is used to identify spectral based model, while neural network is trained to approximate uncertain nonlinear terms. The simulation for spatio-temperature evolution of catalytic rod are presented to show the effectiveness of this low dimensional approximation strategy.