Geodesic
An open-loop criterion for the solvability of a closed-loop guidance problem with incomplete information. Linear control systems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 132-147 Cet article a éte moissonné depuis la source Math-Net.Ru

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The method of open-loop control packages is a tool for stating the solvability of guaranteed closed-loop control problems under incomplete information on the observed states. In this paper, the method is specified for the problem of guaranteed closed-loop guidance of a linear control system to a convex target set at a prescribed point in time. It is assumed that the observed signal on the system's states is linear and the set of its admissible initial states is finite. It is proved that the problem under consideration is equivalent to the problem of open-loop guidance of an extended linear control system to an extended convex target set. Using a separation theorem for convex sets, a solvability criterion is derived, which reduces to a solution of a finite-dimensional optimization problem. An illustrative example is considered.
Keywords: control, incomplete information, linear systems. 
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A. V. Kryazhimskiy; N. V. Strelkovskiy. An open-loop criterion for the solvability of a closed-loop guidance problem with incomplete information. Linear control systems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 132-147. http://geodesic.mathdoc.fr/item/TIMM_2014_20_3_a8/

[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. Zadacha o minimume garantirovannogo rezultata, Nauka, M., 1985, 516 pp. | MR

[4] Krasovskii N. N., Subbotin A. I., Game-theoretical control problems, Springer Verlag, N.Y., 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. matematiki 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] Elliott R. J., Kalton N., “Values in differential games”, Bull. Amer. Math. Soc., 78:3 (1972), 427–431 | DOI | MR | Zbl

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

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

[17] 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

[18] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp. | MR