Least Squares Support Vector MachineBased Multivariate Generalized Predictive Control for Parabolic Distributed Parameter Systems with Control Constraints
Abstract
:1. Introduction
2. System Description
3. Model Reduction by POD and LSSVM
Algorithm 1 Proper Orthogonal Decomposition (POD) basis of rank ℓ 
Require: Snapshots ${\left\{y(\xb7,t)\right\}}_{j=1}^{M}\subset {\Re}^{M},POD\phantom{\rule{4pt}{0ex}}rank\phantom{\rule{4pt}{0ex}}\ell \le M$, where ℓ is the rank of the POD basis.

4. POD and LSSVMBased Multivariate GPC
4.1. Multivariate GPC Strategy
Algorithm 2 The POD and leastsquares support vector machine (LSSVM)based multivariate generalized predictive control (GPC). 
Require: A set of output $y({x}_{m},{t}_{n})$ is derived by appropriate excitation signals.

4.2. The Stability Analysis
5. Case Study
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ARX  Autoregressive exogenous 
DPS  Distributed parameter systems 
GPC  Generalized predictive control 
KL  KarhunenLoève 
LPS  Lumped parameter systems 
LS  Least squares 
PCA  Principal component analysis 
PDE  Partial differential equation 
POD  Proper orthogonal decomposition 
SVM  Support vector machine 
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Ai, L.; Xu, Y.; Deng, L.; Teo, K.L. Least Squares Support Vector MachineBased Multivariate Generalized Predictive Control for Parabolic Distributed Parameter Systems with Control Constraints. Symmetry 2021, 13, 453. https://doi.org/10.3390/sym13030453
Ai L, Xu Y, Deng L, Teo KL. Least Squares Support Vector MachineBased Multivariate Generalized Predictive Control for Parabolic Distributed Parameter Systems with Control Constraints. Symmetry. 2021; 13(3):453. https://doi.org/10.3390/sym13030453
Chicago/Turabian StyleAi, Ling, Yang Xu, Liwei Deng, and Kok Lay Teo. 2021. "Least Squares Support Vector MachineBased Multivariate Generalized Predictive Control for Parabolic Distributed Parameter Systems with Control Constraints" Symmetry 13, no. 3: 453. https://doi.org/10.3390/sym13030453