A problem of robust control of a system with time delay

Marina Blizorukova; Franz Kappel; Vyacheslav Maksimov

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 4, page 821-834
  • ISSN: 1641-876X

Abstract

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A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part' of coordinates) is designed. The algorithm is stable with respect to informational noises and computational errors.

How to cite

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Blizorukova, Marina, Kappel, Franz, and Maksimov, Vyacheslav. "A problem of robust control of a system with time delay." International Journal of Applied Mathematics and Computer Science 11.4 (2001): 821-834. <http://eudml.org/doc/207533>.

@article{Blizorukova2001,
abstract = {A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part' of coordinates) is designed. The algorithm is stable with respect to informational noises and computational errors.},
author = {Blizorukova, Marina, Kappel, Franz, Maksimov, Vyacheslav},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {system with time delay; robust control; reachability},
language = {eng},
number = {4},
pages = {821-834},
title = {A problem of robust control of a system with time delay},
url = {http://eudml.org/doc/207533},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Blizorukova, Marina
AU - Kappel, Franz
AU - Maksimov, Vyacheslav
TI - A problem of robust control of a system with time delay
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 4
SP - 821
EP - 834
AB - A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part' of coordinates) is designed. The algorithm is stable with respect to informational noises and computational errors.
LA - eng
KW - system with time delay; robust control; reachability
UR - http://eudml.org/doc/207533
ER -

References

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  1. Bernier C. and Manitius A. (1978): On semigroups in R^n × L^p corresponding to differential equations with delays. - Can. J. Math., Vol.30, No.5, pp.897-914. Zbl0368.47026
  2. Blizorukova M.S. (2000): On the modelling of an input in a system with time delay. - Prikl. Matem. Informatika, No.5, pp.105-115 (in Russian). 
  3. Kappel F. and Maksimov V. (2000): Robust dynamic input reconstruction for delay systems. - Int. J. Appl. Math. Comp. Sci., Vol.10, No.2, pp.283-307. Zbl0963.93043
  4. Krasovskii A.N. and Krasovskii N.N. (1995): Control under Lack of Information. - New York: Birkhauser. Zbl0827.93001
  5. Krasovskii N.N. (1985): Dynamic System Control. - Moscow: Nauka (in Russian). 
  6. Krasovskii N.N. (1998): Problems of Control and Stabilization of Dynamic Systems. - Summaries of Science and Engineering, Modern Mathematics and Applications, Reviews, Vol.60, pp.24-41, Moscow: VINITI (inRussian). 
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  8. Krasovskii N.N. and Subbotin A.I. (1988): Game-Theoretical Control Problems. - Berlin: Springer. 
  9. Kryazhimskii A. V. and Osipov Yu. S. (1988): On methods of positional modelling controls in dynamic systems, In: Qualitative equations of the Theory of Differential Equations and Controlled Systems. - Sverdlovsk: Academic Press, pp.34-44 (in Russian). 
  10. Maksimov V.I. (1978): On the existence of a saddle point in a difference-differential guidance-deviation game. - Prikl. Matem. Mekh., Vol.42, No.1 (in Russian). 
  11. Maksimov V. (1994): Control reconstruction for nonlinear parabolic equations. - IIASA Working Paper WP-94-04, IIASA, Laxenburg, Austria. 
  12. Osipov Yu.S. (1971a): Differential games for hereditary systems. - Dokl. Akad. Nauk SSSR, Vol.196, No.4, pp.779-782 (in Russian). 
  13. Osipov Yu.S. (1971b): On the theory of differential games for hereditary systems. - Prikl. Matem. Mekh., Vol.35, No.1, pp.123-131 (in Russian). 
  14. Osipov Yu.S. and Kryazhimskii A.V. (1995): Inverse Problems of Ordinary Differential Equations: Dynamical Solutions. - London: Gordon and Breach. Zbl0884.34015
  15. Osipov Yu.S., Kryazhimskii A.V. and Maksimov V.I. (1991): Dynamic Regularization Problems for Distributed Parameter Systems. - Sverdlovsk: Institute of Mathematics and Mechanics, (in Russian). 

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