Application and comparison of kernel functions for linear parameter varying model approximation of nonlinear systems

Abstract

In this paper, a comparative study for kernel-PCA based linear parameter varying (LPV) model approximation of sufficiently nonlinear and reasonably practical systems is carried out. Linear matrix inequalities (LMIs) to be solved in LPV controller design process increase exponentially with the increase in a number of scheduling variables. Fifteen kernel functions are used to obtain the approximate LPV model of highly coupled nonlinear systems. An error to norm ratio of original and approximate LPV models is introduced as a measure of accuracy of the approximate LPV model. Simulation examples conclude the effectiveness of kernel-PCA for LPV model approximation as with the identification of accurate approximate LPV model, computation complexity involved in LPV controller design is decreased exponentially.