Geodesic
On optimality conditions for the guaranteed result in control problems for time-delay systems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 3, pp. 158-169
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For control problems under disturbance of dynamical systems described by differential equations with discrete and distributed time delays and with initial data satisfying the Lipschitz property, the corresponding Lipschitzness of the optimal guaranteed result functional is established and inequalities for its directional derivatives are obtained.
Keywords: optimal control, differential games, time-delay systems. 
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N. Yu. Lukoyanov. On optimality conditions for the guaranteed result in control problems for time-delay systems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 3, pp. 158-169. http://geodesic.mathdoc.fr/item/TIMM_2009_15_3_a11/

[1] Pontryagin L. S. i dr., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1961, 392 pp. | MR | Zbl

[2] Bellman R., Kalaba R., Dinamicheskoe programmirovanie i sovremennaya teoriya upravleniya, Nauka, M., 1969, 118 pp. | Zbl

[3] Aizeks R., Differentsialnye igry, Mir, M., 1967, 479 pp. | MR

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

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

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

[7] Lions P.-L., Souganidis P. E., “Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs's equations”, SIAM J. Contr. Optim., 23:4 (1985), 566–583 | DOI | MR | Zbl

[8] Subbotin A. I., Generalized solutions of first-order PDEs: The dynamical optimization perspective, Birkhäuser, Boston, 1995, 312 pp. | MR

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

[10] Krasovskii N. N., “O primenenii vtorogo metoda A. M. Lyapunova dlya uravnenii s zapazdyvaniyami vremeni”, Prikl. matematika i mekhanika, 20:3. (1956), 315–327 | MR

[11] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959, 211 pp. | MR

[12] Krasovskii N. N., “K zadache unifikatsii differentsialnykh igr”, Dokl. AN SSSR, 226:6 (1976), 1260–1263 | MR

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

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

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

[16] Kim A. V., Functional differential equations. Application of $i$-smooth calculus, Kluwer, Dordrecht, 1999, 165 pp. | MR

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

[18] Lukoyanov N. Yu., “Differentsialnye neravenstva dlya negladkogo funktsionala tseny v zadachakh upravleniya sistemami s posledeistviem”, Tr. In-ta matematiki i mekhaniki UrO RAN, 12, no. 2, Ekaterinburg, 2006, 108–118 | MR | Zbl

[19] Lukoyanov N., “On dynamical optimization of conflict hereditary systems”, Proc. of the 17-th IFAC world congress, Vol. 17, part 1, 2008, 11357–11362; http://www.ifac-papersonline.net

[20] Arkin V. I., Levin V. L., “Vypuklost znachenii vektornykh integralov, teoremy izmerimogo vybora i variatsionnye zadachi”, Uspekhi mat. nauk, 27:3(165) (1972), 21–77 | MR | Zbl

[21] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985, 225 pp. | MR

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

[23] Kurzhanskii A. B., “Ob analiticheskom opisanii puchka vyzhivayuschikh traektorii differentsialnoi sistemy”, Dokl. AN SSSR, 287:5 (1986), 1047–1050 | MR

[24] Haddad G., “Monotone trajectories of differential inclusions and functional differential inclusions with memory”, Israel J. Math., 39 (1981), 83–100 | DOI | MR | Zbl

[25] Aubin J. P., Viability theory, Birkhäuser, Boston, 1991, 544 pp. | MR | Zbl