Geodesic
Differential inequalities for a nonsmooth value functional in control systems with an aftereffect
Trudy Instituta matematiki i mehaniki, Control, stability, and inverse problems of dynamics, Tome 12 (2006) no. 2, pp. 108-118 Cet article a éte moissonné depuis la source Math-Net.Ru

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Functional differential inequalities, uniquely describing the optimal guaranteed result, are obtained for a control system with aftereffect, in the presence of disturbances. Specific forms of these inequalities are given for typical particular cases. 
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N. Yu. Lukoyanov. Differential inequalities for a nonsmooth value functional in control systems with an aftereffect. Trudy Instituta matematiki i mehaniki, Control, stability, and inverse problems of dynamics, Tome 12 (2006) no. 2, pp. 108-118. http://geodesic.mathdoc.fr/item/TIMM_2006_12_2_a9/

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

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

[3] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959 | MR

[4] Osipov Yu. S., “Differentsialnaya igra navedeniya dlya sistem s posledeistviem”, Prikl. matematika i mekhanika, 35:1 (1971), 123–131 | MR | Zbl

[5] Osipov Yu. S., “Differentsialnye igry sistem s posledeistviem”, Dokl. AN SSSR, 196:4 (1971), 779–782 | MR | Zbl

[6] Kim A. V., Functional Differential Equations. Application of $i$-Smooth Calculus, Kluwer, Dordrecht, 1999 | MR

[7] Soner H. M., “On the HamiltonvJacobivBellman equations in Banach spaces”, J. Optim. Theory and Appl., 57:3 (1988), 429–437 | DOI | MR | Zbl

[8] Crandall M. G., Lions P.-L., “HamiltonvJacobi equations in infinite dimensions. Part IV: Hamiltonians with unbounded linear terms”, J. Funct. Anal., 90 (1990), 237–283 | DOI | MR | Zbl

[9] Wolenski P. R., “HamiltonvJacobi theory for hereditary control problems”, Nonlinear Anal., 22:7 (1994), 875–894 | DOI | MR | Zbl

[10] Lukoyanov N. Yu., “Funktsionalnye uravneniya tipa Gamiltona–Yakobi i differentsialnye igry s nasledstvennoi informatsiei”, Dokl. RAN, 371:4 (2000), 457–461 | MR | Zbl

[11] Clarke F. H., Ledyaev Yu. S., Stern R. J., Wolenski P. R., Nonsmooth Analysis and Control Theory, Springer, New York, 1998 | MR

[12] Demyanov V. F., Rubinov A. M., Osnovy negladkogo analiza ikvazidifferentsialnoe ischislenie, Nauka, M., 1990 | MR

[13] Pshenichnyi B. N., Neobkhodimye usloviya ekstremuma, Nauka, M., 1982 | MR

[14] Lukoyanov N. Yu., “O svoistvakh funktsionala tseny differentsialnoi igry s nasledstvennoi informatsiei”, Prikl. matematika i mekhanika, 65:3 (2001), 375–384 | MR | Zbl

[15] Subbotin A. I., Generalized Solutions of First-Order PDEs, Birkhäuser, Boston, 1995 | MR

[16] Lukoyanov N. Yu., “Functional Hamilton–Jacobi type equations in $ci$-derivatives for systems with distributed delays”, Nonlinear Funct. Anal. and Appl., 8:3 (2003), 365–397 | MR | Zbl

[17] Subbotin A. I., “Obobschenie osnovnogo uravneniya teorii differentsialnykh igr”, Dokl. AN SSSR, 254:2 (1980), 293–297 | MR | Zbl

[18] Lukoyanov N. Yu., “Strategii pritselivaniya v napravlenii invariantnykh gradientov”, Prikl. matematika i mekhanika, 68:4 (2004), 629–643 | MR | Zbl

[19] Crandall M. G., Ishii H., Lions P.-L., “Uniqueness of viscosity solutions of Hamilton–Jacobi equations revisited”, J. Math. Soc. Japan, 39:4 (1987), 581–596 | DOI | MR | Zbl

[20] Warga J., Optimal Control of Differential and Functional Equations, Acad. Press, New York, 1972 | MR | Zbl

[21] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985 | MR