Pontryagin's Alternated Integral in the Theory of Control Synthesis

A. B. Kurzhanskii

Informatics and Automation, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 234-248.

Bibliographie

[1] Aubin J.-P., Frankowska H., Set-valued analysis, Birkhäuser, Boston, 1990 | MR | Zbl

[2] Bardi M., Capuzzo-Dolcetta I., Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations, Birkhäuser, Boston, 1997 | MR | Zbl

[3] Basar T., Bernhard P., $H^{\infty}$ optimal control and related minimax design problems, 2nd ed., Birkhäuser, Boston, 1995 | MR

[4] Chernousko F. L., State estimation for dynamic systems, CRC Press, Singapore, 1994

[5] Crandall M. G., Lions P. L., “Viscosity solutions of Hamilton–Jacobi equations”, Trans. Amer. Math. Soc., 277 (1983), 1–42 | DOI | MR | Zbl

[6] Fleming W. H., Soner H. M., Controlled Markov processes and viscosity solutions, Springer, N. Y. etc., 1993 | MR | Zbl

[7] Knobloch H., Isidori A., Flockerzi D., Topics in control theory, DMV-Seminar, 22, Birkhäuser, Boston etc., 1993 | MR | Zbl

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

[9] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1986 | MR

[10] Krasovski N. N., Subbotin A. I., Positional differential games, Springer, N. Y. etc., 1988

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

[12] Kurzhanskii A. B., Nikonov O. I., “O zadache sinteza strategii upravleniya. Evolyutsionnye uravneniya i mnogoznachnoe integrirovanie”, DAN SSSR, 311 (1990), 788–793 | MR

[13] Kurzhanskii A. B., Nikonov O. I., “Evolyutsionnye uravneniya dlya trubok traektorii sintezirovannykh sistem upravleniya”, Dokl. RAN, 48:3 (1994), 606–611 | MR

[14] Kurzhanski A. B., Vályi I., Ellipsoidal calculus for estimation and control, Birkhäuser, Boston, 1996 | MR

[15] Lions P-L., Souganidis P. E., “Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaac's Equations”, SIAM J. Contr. Optim., 23 (1985), 566–583 | DOI | MR | Zbl

[16] Mischenko E. F., “Zadachi presledovaniya i ukloneniya ot vstrechi v teorii differentsialnykh igr”, Izv. AN SSSR. Tekhn. kibernetika, 1971, no. 5, 3–9

[17] Nikolskii M. S., “O nizhnem alternirovannom integrale Pontryagina v lineinykh differentsialnykh igrakh presledovaniya”, Mat. sb., 128:1 (1985), 35–49 | MR

[18] Pontryagin L. S., “O lineinykh differentsialnykh igrakh. I, II”, DAN SSSR, 8 (1967), 769–771 ; 910–912 | Zbl | Zbl

[19] Pontryagin L. S., “Lineinye differentsialnye igry presledovaniya”, Mat. sb., 112:3 (1980), 307–330 | MR | Zbl

[20] Rockafellar R. T., Convex analysis, Princeton Univ. Press, 1970 | MR

[21] Subbotin A. I., Generalized solutions of first-order PDE's. The dynamic optimization perspective, Birkhäuser, Boston, 1995 | MR

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

[23] Varaiya P., Lin J. C., “Existence of saddle points in differential games”, SIAM J. Contr. Optim., 7:1 (1969), 142–157