An application of the Fourier transform to optimization of continuous 2-D systems

Vitali Dymkou; Michael Dymkov

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 1, page 45-54
  • ISSN: 1641-876X

Abstract

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This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.

How to cite

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Dymkou, Vitali, and Dymkov, Michael. "An application of the Fourier transform to optimization of continuous 2-D systems." International Journal of Applied Mathematics and Computer Science 13.1 (2003): 45-54. <http://eudml.org/doc/207622>.

@article{Dymkou2003,
abstract = {This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.},
author = {Dymkou, Vitali, Dymkov, Michael},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Fourier transform; optimization; approximation; 2D systems; entire functions; 2-D systems},
language = {eng},
number = {1},
pages = {45-54},
title = {An application of the Fourier transform to optimization of continuous 2-D systems},
url = {http://eudml.org/doc/207622},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Dymkou, Vitali
AU - Dymkov, Michael
TI - An application of the Fourier transform to optimization of continuous 2-D systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 1
SP - 45
EP - 54
AB - This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.
LA - eng
KW - Fourier transform; optimization; approximation; 2D systems; entire functions; 2-D systems
UR - http://eudml.org/doc/207622
ER -

References

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  5. Dymkov M. (2001): Entire function methods for optimization problems in continuous-discrete 2D control systems, In: Multidimensional Signal, Circuits and Systems(K. Gałkowski and J. Wood, Eds.). - London: Taylor and Francis, pp. 171-182. 
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  13. Khurgin Ya.I. and Yakovlev V.P. (1971): Finite Functions in Physics and Technics. - Moscow: Nauka, (in Russian). 
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