Geodesic
On a Mutual Tracking Block for the Real Object and its Virtual Model-Leader
Contributions to game theory and management, Tome 6 (2013), pp. 248-252 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The research is devoted to a feedback control problem of stochastic stable mutual tracking for motions of a real dynamical object, and some virtual computer simulated model-leader, under dynamical and informational disturbances. The control and disturbance actions in the model are determined by proposed random tests. To obtain solution to the considered problem we apply the so-called extremal minimax and maximin shift conditions. Theoretical results are illustrated by numerical simulations.
Keywords: feedback control, nonlinear system, extremal shift. 
@article{CGTM_2013_6_a17,
     author = {Andrew N. Krasovskii},
     title = {On a {Mutual} {Tracking} {Block} for the {Real} {Object} and its {Virtual} {Model-Leader}},
     journal = {Contributions to game theory and management},
     pages = {248--252},
     year = {2013},
     volume = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2013_6_a17/}
}
TY  - JOUR
AU  - Andrew N. Krasovskii
TI  - On a Mutual Tracking Block for the Real Object and its Virtual Model-Leader
JO  - Contributions to game theory and management
PY  - 2013
SP  - 248
EP  - 252
VL  - 6
UR  - http://geodesic.mathdoc.fr/item/CGTM_2013_6_a17/
LA  - en
ID  - CGTM_2013_6_a17
ER  - 
%0 Journal Article
%A Andrew N. Krasovskii
%T On a Mutual Tracking Block for the Real Object and its Virtual Model-Leader
%J Contributions to game theory and management
%D 2013
%P 248-252
%V 6
%U http://geodesic.mathdoc.fr/item/CGTM_2013_6_a17/
%G en
%F CGTM_2013_6_a17
Andrew N. Krasovskii. On a Mutual Tracking Block for the Real Object and its Virtual Model-Leader. Contributions to game theory and management, Tome 6 (2013), pp. 248-252. http://geodesic.mathdoc.fr/item/CGTM_2013_6_a17/

[1] Bellman R., Dynamic Programming, Princeton University Press, Princeton, NJ, 1957 | MR | Zbl

[2] Isaacs R., Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, J. Wiley and Sons, New York, 1965 | MR | Zbl

[3] J. Appl. Math. Mech., 44 (1980), 425–430 | DOI | MR

[4] Krasovskii A.Ṅ., Krasovskii N. N., Control under Lack of Information, Birkhauser, Boston, 1994 | Zbl

[5] Krasovskii A. N., Choi Y. S., Stochastic Control with the Leaders-Stabilizers, Preprint, Inst. Math. Mech., Ural Branch Russ. Akad. Sci., Yekaterinburg, 2001

[6] Game-Theoretical Control Problems, Springer, New York, 1988 | MR | MR | Zbl

[7] Kurzhanski A. B., Control and Observation under Uncertainty Conditions, Nauka, M., 1977 | Zbl

[8] Liptser R. S., Shiryaev A. N., Statistics of Random Processes: Nonlinear Filtration and Related Problems, Nauka, M., 1974 ; Engl. transl.: Statistics of Random Processes, v. 1, General Theory; v. 2, Applications, Springer, Berlin, 2001 | MR | Zbl

[9] McKinsey J. C., Introduction to the Theory of Games, McGraw-Hill, New York, 1952 | MR | Zbl

[10] Autom. Remote Control, 33, 1424–1429 | MR | Zbl

[11] Osipov Yu. S., Kryazhimskii A. V., Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, Gordon and Breach, Amsterdam, 1995 | MR | Zbl

[12] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E.Ḟ., The Mathematical Theory of Optimal Processes, Fizmatgiz, M., 1961 ; Interscience, New York, 1962 | MR