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.
@article{bwmeta1.element.bwnjournal-article-amcv13i1p45bwm,
author = {Dymkou, Vitali and Dymkov, Michael},
title = {An application of the Fourier transform to optimization of continuous 2-D systems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {13},
year = {2003},
pages = {45-54},
zbl = {1046.93030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv13i1p45bwm}
}
Dymkou, Vitali; Dymkov, Michael. An application of the Fourier transform to optimization of continuous 2-D systems. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) pp. 45-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv13i1p45bwm/
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