# An infinite horizon predictive control algorithm based on multivariable input-output models

• Volume: 14, Issue: 2, page 167-180
• ISSN: 1641-876X

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## Abstract

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In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.

## How to cite

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Ławryńczuk, Maciej, and Tatjewski, Piotr. "An infinite horizon predictive control algorithm based on multivariable input-output models." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 167-180. <http://eudml.org/doc/207688>.

@article{Ławryńczuk2004,
abstract = {In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.},
author = {Ławryńczuk, Maciej, Tatjewski, Piotr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {infinite horizon; model predictive control; quadratic programming; singular-value decomposition; stability; predictive control; input-output models; matrix Diophantine equations; constrained control; response calculation},
language = {eng},
number = {2},
pages = {167-180},
title = {An infinite horizon predictive control algorithm based on multivariable input-output models},
url = {http://eudml.org/doc/207688},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Ławryńczuk, Maciej
AU - Tatjewski, Piotr
TI - An infinite horizon predictive control algorithm based on multivariable input-output models
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 2
SP - 167
EP - 180
AB - In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.
LA - eng
KW - infinite horizon; model predictive control; quadratic programming; singular-value decomposition; stability; predictive control; input-output models; matrix Diophantine equations; constrained control; response calculation
UR - http://eudml.org/doc/207688
ER -

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