Geodesic
On the solvability of problems of guaranteeing control for partially observable linear dynamical systems
Informatics and Automation, Mathematical control theory and differential equations, Tome 277 (2012), pp. 152-167.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to a specification of the method of open-loop control packages, a universal instrument for verification of the solvability of problems of closed-loop control for partially observable dynamical systems. Under the assumption that the control system and observed signal are linear and the set of the admissible initial states is finite, a structure of the corresponding open-loop control packages is specified and a finite-step backward construction is described, which provides a criterion for the solvability of a problem of guaranteed closed-loop guidance onto a target set at a prescribed time. 
@article{TRSPY_2012_277_a9,
     author = {A. V. Kryazhimskiy and Yu. S. Osipov},
     title = {On the solvability of problems of guaranteeing control for partially observable linear dynamical systems},
     journal = {Informatics and Automation},
     pages = {152--167},
     publisher = {mathdoc},
     volume = {277},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_277_a9/}
}
TY  - JOUR
AU  - A. V. Kryazhimskiy
AU  - Yu. S. Osipov
TI  - On the solvability of problems of guaranteeing control for partially observable linear dynamical systems
JO  - Informatics and Automation
PY  - 2012
SP  - 152
EP  - 167
VL  - 277
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2012_277_a9/
LA  - ru
ID  - TRSPY_2012_277_a9
ER  - 
%0 Journal Article
%A A. V. Kryazhimskiy
%A Yu. S. Osipov
%T On the solvability of problems of guaranteeing control for partially observable linear dynamical systems
%J Informatics and Automation
%D 2012
%P 152-167
%V 277
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2012_277_a9/
%G ru
%F TRSPY_2012_277_a9
A. V. Kryazhimskiy; Yu. S. Osipov. On the solvability of problems of guaranteeing control for partially observable linear dynamical systems. Informatics and Automation, Mathematical control theory and differential equations, Tome 277 (2012), pp. 152-167. http://geodesic.mathdoc.fr/item/TRSPY_2012_277_a9/

[1] Osipov Yu.S., “Pakety programm: podkhod k resheniyu zadach pozitsionnogo upravleniya s nepolnoi informatsiei”, UMN, 61:4 (2006), 25–76 | DOI | MR | Zbl

[2] Kryazhimskii A.V., Osipov Yu.S., “Idealizirovannye pakety programm i zadachi pozitsionnogo upravleniya s nepolnoi informatsiei”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15:3 (2009), 139–157

[3] Krasovskii N.N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970 | MR | Zbl

[4] Krasovskii N.N., Subbotin A.I., Game-theoretical control problems, Springer, New York, 1988 | MR | MR | Zbl | Zbl

[5] Krasovskii N.N., Upravlenie dinamicheskoi sistemoi: Zadacha o minimume garantirovannogo rezultata, Nauka, M., 1985 | MR

[6] Krasovskii A.N., Krasovskii N.N., Control under lack of information, Birkhäuser, Boston, 1995 | MR

[7] Subbotin A.I., Minimaksnye neravenstva i uravneniya Gamiltona–Yakobi, Nauka, M., 1991 | MR | Zbl

[8] Subbotin A.I., Generalized solutions of first-order PDEs: The dynamical optimization perspective, Birkhäuser, Boston, 1995 | MR

[9] Subbotin A.I., Chentsov A.G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981 | MR | Zbl

[10] Chentsov A.G., “Metod programmnykh iteratsii v abstraktnykh zadachakh upravleniya”, PMM, 68:4 (2004), 573–585 | MR | Zbl

[11] Roxin E., “Axiomatic approach in differential games”, J. Optim. Theory Appl., 3 (1969), 153–163 | DOI | MR | Zbl

[12] Ryll-Nardzewski C., “A theory of pursuit and evasion”, Advances in game theory, Ann. Math. Stud., 52, Princeton Univ. Press, Princeton, 1964, 113–126 | MR