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.
@article{bwmeta1.element.bwnjournal-article-amcv11i4p821bwm,
author = {Blizorukova, Marina and Kappel, Franz and Maksimov, Vyacheslav},
title = {A problem of robust control of a system with time delay},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {11},
year = {2001},
pages = {821-834},
zbl = {0995.93040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p821bwm}
}
Blizorukova, Marina; Kappel, Franz; Maksimov, Vyacheslav. A problem of robust control of a system with time delay. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 821-834. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p821bwm/
[000] 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. | Zbl 0368.47026
[001] 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).
[002] 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. | Zbl 0963.93043
[003] Krasovskii A.N. and Krasovskii N.N. (1995): Control under Lack of Information. - New York: Birkhauser. | Zbl 0827.93001
[004] Krasovskii N.N. (1985): Dynamic System Control. - Moscow: Nauka (in Russian).
[005] 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).
[006] Krasovskii N.N. and Lukoyanov N. Yu. (1996): Problems of conflict control with hereditary information. - Prikl. Matem. Mekh., Vol.60, No.6, pp.885-900 (in Russian).
[007] Krasovskii N.N. and Subbotin A.I. (1988): Game-Theoretical Control Problems. - Berlin: Springer.
[008] 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).
[009] 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).
[010] Maksimov V. (1994): Control reconstruction for nonlinear parabolic equations. - IIASA Working Paper WP-94-04, IIASA, Laxenburg, Austria.
[011] Osipov Yu.S. (1971a): Differential games for hereditary systems. - Dokl. Akad. Nauk SSSR, Vol.196, No.4, pp.779-782 (in Russian).
[012] 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).
[013] Osipov Yu.S. and Kryazhimskii A.V. (1995): Inverse Problems of Ordinary Differential Equations: Dynamical Solutions. - London: Gordon and Breach. | Zbl 0884.34015
[014] 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).