Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/application-and-comparison-of-kernel-functions-for-linear-parameter-fVXYRrNJoq
References (25)
-
H. Abbas, Ahsan Ali, S. Hashemi, H. Werner (2014)
LPV state-feedback control of a control moment gyroscopeControl Engineering Practice, 24
-
Thomas Hofmann, B. Scholkopf, Alex Smola (2007)
Kernel methods in machine learningAnnals of Statistics, 36
-
(1999)
Manual For Model 750: Control Moment Gyroscope, Educ Control Prod Bell Canyon -
Tong Zhang (2001)
An Introduction to Support Vector Machines and Other Kernel-Based Learning MethodsAI Mag., 22
-
W. Rugh, J. Shamma (2000)
Research on gain schedulingAutom., 36
-
(2013)
Two Rotor Aero-Dynamical System User's Manual, INTECO -
B. Scholkopf, Alex Smola, K. Müller (1998)
Nonlinear Component Analysis as a Kernel Eigenvalue ProblemNeural Computation, 10
-
M. Meisami-Azad, J. Mohammadpour, K. Grigoriadis, M. Harold, M. Franchek (2011)
PCA-based linear parameter varying control of SCR aftertreatment systemsProceedings of the 2011 American Control Conference
-
A. Bachnas (2012)
Linear Parameter Varying Modeling of a High-Purity Distillation Column -
S. Ounpraseuth (2008)
Gaussian Processes for Machine LearningJournal of the American Statistical Association, 103
-
Muhammad Siraj, R. Tóth, S. Weiland (2012)
Joint order and dependency reduction for LPV state-space models2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
-
R. Tóth, H. Abbas, H. Werner (2012)
On the State-Space Realization of LPV Input-Output Models: Practical ApproachesIEEE Transactions on Control Systems Technology, 20
-
H. Sahbi, F. Fleuret (2001)
Scale-Invariance of Support Vector Machines based on the Triangular Kernel -
유정완 (2011)
Learning with Kernels, 59
-
B. Scholkopf, Alex Smola, K. Müller (1997)
Kernel Principal Component Analysis -
(1997)
K R Müller -
B. Wie (1998)
Space Vehicle Dynamics and Control -
P. Chalupa, J. Novák, J. Přikryl (2016)
Design and verification of a robust controller for the twin rotor MIMO system -
P. Cochat, L. Vaucoret, J. Sarles (2008)
Et alEvidence Based Mental Health, 11
-
Amir Atiya (2005)
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and BeyondIEEE Transactions on Neural Networks, 16
-
(1998)
B Schölkopf -
S. Rizvi, J. Mohammadpour, R. Tóth, N. Meskin (2016)
A Kernel-Based PCA Approach to Model Reduction of Linear Parameter-Varying SystemsIEEE Transactions on Control Systems Technology, 24
-
F. Saleem, Ahsan Ali, Muhammad Wasim, I. Shaikh (2019)
An Iterative Kernel-PCA Based LPV Control Approach for a 4-DOF Control Moment GyroscopeIEEE Access, 7
-
A. Kwiatkowski, H. Werner (2008)
PCA-Based Parameter Set Mappings for LPV Models With Fewer Parameters and Less OverboundingIEEE Transactions on Control Systems Technology, 16
-
Hsuan-Tien Lin (2005)
A Study on Sigmoid Kernels for SVM and the Training of non-PSD Kernels by SMO-type Methods
- 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