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

Application and comparison of kernel functions for linear parameter varying model approximation... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © Editorial Committee of Applied Mathematics 2023
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-023-3965-8
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics-A Journal of Chinese Universities – Springer Journals

Published: Mar 1, 2023

Keywords: kernel-PCA; LMIs; LPV; error to norm ratio; computational complexity; and control design; 93Cxx

References

  • PCA-based parameter set mappings for LPV models with fewer parameters and less overbounding
    Kwiatkowski, A; Werner, H
  • On the state-space realization of LPV input-output models: Practical approaches
    Toth, R; Abbas, H S; Werner, H
  • Nonlinear component analysis as a kernel eigenvalue problem
    Schölkopf, B; Smola, A; Müller, K R
  • A study on sigmoid kernels for SVM and the training of non-PSD kernels by SMO-type methods
    Lin, H T; Lin, C J
  • An Iterative Kernel-PCA based LPV Control Approach for a 4-DOF Control Moment Gyroscope
    Saleem, F; Ali, A; Wasim, M; Shaikh, I