Geodesic
Control packages: an approach to solution of positional control problems with incomplete information
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 4, pp. 611-661 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An approach is proposed for solving problems of positional control of a dynamical system under conditions of incomplete information about its current phase states. The basis of this approach is a new notion of control packages, namely, procedures for constructing control programs which are non-anticipatory with respect to the dynamics of observations. For definiteness, the approach is realised for a concrete control problem of guaranteed guidance of a controlled system to a given target set at a fixed moment of time. The main result of the paper states that the indicated problem is soluble in the class of positional strategies if and only if it is soluble in the class of control packages. This result shows a way to reduce control problems in the positional (closed-loop) formulation to control problems in the program (open-loop) formulation. In this sense a methodology for program constructions is developed that is well known in the theory of positional differential games. 
@article{RM_2006_61_4_a3,
     author = {Yu. S. Osipov},
     title = {Control packages: an approach to solution of positional control problems with incomplete information},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {611--661},
     year = {2006},
     volume = {61},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2006_61_4_a3/}
}
TY  - JOUR
AU  - Yu. S. Osipov
TI  - Control packages: an approach to solution of positional control problems with incomplete information
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2006
SP  - 611
EP  - 661
VL  - 61
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/RM_2006_61_4_a3/
LA  - en
ID  - RM_2006_61_4_a3
ER  - 
%0 Journal Article
%A Yu. S. Osipov
%T Control packages: an approach to solution of positional control problems with incomplete information
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2006
%P 611-661
%V 61
%N 4
%U http://geodesic.mathdoc.fr/item/RM_2006_61_4_a3/
%G en
%F RM_2006_61_4_a3
Yu. S. Osipov. Control packages: an approach to solution of positional control problems with incomplete information. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 4, pp. 611-661. http://geodesic.mathdoc.fr/item/RM_2006_61_4_a3/

[1] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelizde, E. F. Mischenko, Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961 | MR | Zbl

[2] R. Aizeks, Differentsialnye igry, Mir, M., 1967 | MR | MR | Zbl

[3] L. S. Pontryagin, “O lineinykh differentsialnykh igrakh. II”, Dokl. AN SSSR, 175:4 (1967), 764–766 | MR | Zbl

[4] L. S. Pontryagin, “Lineinaya differentsialnaya igra ubeganiya”, Sbornik statei, posvyaschennykh I. M. Vinogradovu k ego 80-letiyu, Tr. MIAN, 112, 1971, 30–63 | MR | Zbl

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

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

[7] N. N. Krasovskii, Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985 | MR | Zbl

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

[9] A. N. Krasovskii, N. N. Krasovskii, Control under lack of information, Systems Control Found. Appl., Birkhäuser, Boston, MA, 1995 | MR | Zbl

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

[11] A. I. Subbotin, Generalized solutions of first-order PDEs: The dynamical optimization perspective, Systems Control Found. Appl., Birkhäuser, Boston, MA, 1995 | MR | Zbl

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

[13] A. V. Kryazhimskii, S. D. Filippov, “Ob igrovoi zadache navedeniya dlya dvukh tochek na ploskosti v usloviyakh nepolnoi informatsii”, Zadachi upravleniya pri nepolnoi informatsii, UNTs AN SSSR, Sverdlovsk, 1976, 62–77

[14] V. E. Pak, “Zadacha navedeniya s nepolnoi informatsiei”, Izv. AN SSSR. Ser. tekhn. kibern., 1976, no. 4, 29–36 | MR | Zbl

[15] V. D. Batukhtin, “Ob odnoi igrovoi zadache navedeniya s nepolnoi informatsiei”, Prikl. matem. i mekh., 44:4 (1980), 595–601 | MR | Zbl

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

[17] A. V. Kryazhimskii, “Differentsialnaya igra sblizheniya v usloviyakh nepolnoi informatsii o sisteme”, Ukr. matem. zhurn., 27:4 (1975), 521–526 | MR | Zbl

[18] A. V. Kryazhimskii, “Alternativa v lineinoi igre sblizheniya-ukloneniya s nepolnoi informatsiei”, Dokl. AN SSSR, 230:4 (1976), 773–776 | MR | Zbl

[19] A. A. Kreknin, A. I. Subbotin, “Igrovaya zadacha presledovaniya v usloviyakh nepolnoi fazovoi informatsii o presleduemoi sisteme”, Differentsialnye sistemy upravleniya, Tr. In-ta matem. i mekh. UNTs AN SSSR, 26, UNTs AN SSSR, Sverdlovsk, 1979, 21–33 | MR | Zbl

[20] A. B. Kurzhanskii, “O sinteze upravlenii po rezultatam izmerenii”, Prikl. matem. i mekh., 68:4 (2004), 547–563 | MR | Zbl

[21] Yu. S. Osipov, A. V. Kryazhimskii, Inverse problems for ordinary differential equations: dynamical solutions, Gordon Breach, Basel, 1995 | MR | Zbl

[22] Yu. S. Osipov, F. P. Vasilev, M. M. Potapov, Osnovy metoda dinamicheskoi regulyarizatsii, Izd-vo MGU, M., 1999

[23] A. V. Kryazhimskii, Yu. S. Osipov, “On positional calculation of $\Omega$-normal controls in dynamical systems”, Problems Control Inform. Theory, 13:6 (1984), 425–436 | MR | Zbl

[24] F. Fagnani, V. Maksimov, L. Pandolfi, “A recursive deconvolution approach to disturbance reduction”, IEEE Trans. Automat. Control, 49:6 (2004), 907–921 | DOI | MR

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

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

[27] A. N. Tikhonov, “O funktsionalnykh uravneniyakh tipa Volterra i ikh primenenii k nekotorym zadacham matematicheskoi fiziki”, Byull. MGU, sekts. A, 1938, no. 8, 1–25 | Zbl

[28] A. N. Tikhonov, V. Ya. Arsenin, Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR | Zbl

[29] Dzh. Varga, Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977 | MR | MR | Zbl

[30] A. B. Kurzhanskii, Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977 | MR | Zbl