Transformation of optimal control problems of descriptor systems into problems with state-space systems

Jovan Stefanovski

Kybernetika (2012)

  • Volume: 48, Issue: 6, page 1156-1179
  • ISSN: 0023-5954

Abstract

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We show how we can transform the ℋ ∞ and ℋ 2 control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for ℋ ∞ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal ℋ 2 controller.

How to cite

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Stefanovski, Jovan. "Transformation of optimal control problems of descriptor systems into problems with state-space systems." Kybernetika 48.6 (2012): 1156-1179. <http://eudml.org/doc/251374>.

@article{Stefanovski2012,
abstract = {We show how we can transform the $\{\mathcal \{H\}\}_\infty $ and $\{\mathcal \{H\}\}_2$ control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for $\{\mathcal \{H\}\}_\infty $ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal $\{\mathcal \{H\}\}_2$ controller.},
author = {Stefanovski, Jovan},
journal = {Kybernetika},
keywords = {parametrization of stabilizing controllers; inner matrices; $\{\mathcal \{H\}\}_\infty $ and $\{\mathcal \{H\}\}_2$ control; parametrization of stabilizing controllers; inner matrices; and control},
language = {eng},
number = {6},
pages = {1156-1179},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Transformation of optimal control problems of descriptor systems into problems with state-space systems},
url = {http://eudml.org/doc/251374},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Stefanovski, Jovan
TI - Transformation of optimal control problems of descriptor systems into problems with state-space systems
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 6
SP - 1156
EP - 1179
AB - We show how we can transform the ${\mathcal {H}}_\infty $ and ${\mathcal {H}}_2$ control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for ${\mathcal {H}}_\infty $ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal ${\mathcal {H}}_2$ controller.
LA - eng
KW - parametrization of stabilizing controllers; inner matrices; ${\mathcal {H}}_\infty $ and ${\mathcal {H}}_2$ control; parametrization of stabilizing controllers; inner matrices; and control
UR - http://eudml.org/doc/251374
ER -

References

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