A problem of guaranteed closed-loop guidance by a fixed time for a linear control system with incomplete information. Program solvability criterion
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 168-177 Cet article a éte moissonné depuis la source Math-Net.Ru

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The method of open-loop control packages is applied to identify solvability conditions in a problem of guaranteed closed-loop guidance of a linear partially observed control system to one of convex target sets by a specified time. The set of admissible initial states is assumed to be finite. The task is reduced to a problem of open-loop guidance of an extended control system, and solvability conditions for this system are described in terms of finite-dimensional convex optimization problems.
Keywords: control, incomplete information, linear systems.
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A. V. Kryazhimskii; N. V. Strelkovskii. A problem of guaranteed closed-loop guidance by a fixed time for a linear control system with incomplete information. Program solvability criterion. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 168-177. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a14/

[1] Krasovskii N. N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970, 420 pp. | MR | Zbl

[2] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[3] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 546 pp. | MR

[4] Krasovskii A. N., Subbotin A. I., Game-theoretical control problems, Springer Verlag, New-York, 1988, 517 pp. | MR

[5] Krasovskii A. N., Krasovskii N. N., Control under lack of information, Birkhäuser, Boston, 1995, 322 pp. | MR

[6] Subbotin A. I., Minimaksnye neravenstva i uravneniya Gamiltona–Yakobi, Nauka, M., 1991, 216 pp. | MR | Zbl

[7] Subbotin A. I., Generalized solutions of first-order PDEs, Birkhäuser, Boston, 1995, 312 pp. | MR

[8] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981, 288 pp. | MR | Zbl

[9] Krasovskii N. N., Osipov Yu. S., “Zadacha upravleniya s nepolnoi informatsiei”, Mekhanika tverd. tela, 1973, no. 4, 5–14 | MR

[10] Kurzhanskii A. B., “O sinteze upravlenii po rezultatam nablyudenii”, Prikl. matematika i mekhanika, 68:4 (2004), 547–563 | MR

[11] Osipov Yu. S., “Pakety programm: podkhod k resheniyu zadach pozitsionnogo upravleniya s nepolnoi informatsiei”, Uspekhi mat. nauk, 61:4(370) (2006), 25–76 | DOI | MR | Zbl

[12] 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, no. 3, 2009, 139–157

[13] Kryazhimskii A. V., Osipov Yu. S., “O razreshimosti zadach garantiruyuschego upravleniya dlya chastichno nablyudaemykh lineinykh dinamicheskikh sistem”, Tr. MIAN, 277, 2012, 152–167 | MR

[14] Kryazhimskii A. V., Strelkovskii N. V., “Programmnyi kriterii razreshimosti zadachi pozitsionnogo navedeniya s nepolnoi informatsiei. Lineinye upravlyaemye sistemy”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20, no. 3, 2014, 132–147

[15] Elliott R. J., Kalton N., “Values in differential games”, Bull. Amer. Math. Soc., 78:3 (1972), 291–486 | DOI | MR

[16] Roxin E., “Axiomatic approach in differential games”, J. Opt. Theory Appl., 3 (1969), 156–163 | DOI | MR

[17] Rull-Nardzevski C., “A theory of purcuit and evasion”, Advances in Game Theory, Princeton Univ. Press, Princeton, 1964, 113–126

[18] Quincampoix M., Veliov V., “Optimal control of uncertain systems with incomplete information for the disturbances”, SIAM J. Control Optim., 43:4 (2005), 1373–1399 | DOI | MR | Zbl