Geodesic
Inequalities for subgradients of a value functional in differential games for time-delay systems
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 91-94.

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A two-person zero-sum positional differential game is considered in which the motion of a dynamical system is described by a nonlinear delay equation and the initial motion history is determined by a piecewise continuous function. Inequalities for directional derivatives of the value functional and inequalities for its sub- and supergradients are obtained.
Keywords: differential games, time-delay systems, Hamilton–Jacobi equations, invariant derivatives, subdifferentials, minimax solutions, viscosity solutions. 
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N. Yu. Lukoyanov; A. R. Plaksin. Inequalities for subgradients of a value functional in differential games for time-delay systems. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 91-94. http://geodesic.mathdoc.fr/item/DANMA_2020_490_a20/

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

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

[3] Subbotin A.I., Tarasev A.M., “Sopryazhennye proizvodnye funktsii tseny differentsialnoi igry”, DAN SSSR, 283:3 (1985), 559–564 | MR | Zbl

[4] Guseinov Kh.G., Subbotin A.I., Ushakov V.N., “Proizvodnye mnogoznachnykh otobrazhenii i ikh primenenie v igrovykh zadachakh upravleniya”, Problemy upravleniya i teorii informatsii, 14:3 (1985), 1–14

[5] Subbotin A.I., Generalized Solutions of First-Order PDEs: The Dynamical Optimization Perspective, Birkhäuser, Boston, 1995 | MR

[6] Souganidis P.E., “Max-Min Representations and Product Formulas for Viscosity Solutions of Hamilton-Jacobi Equations with Applications to Differential Games”, Nonlinear Analysis. Theory, Meth., Appl., 9:3 (1985), 217–257 | DOI | MR

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

[8] Subbotin A.I., “Ob odnom svoistve subdifferentsiala”, Matem. sb., 182:9 (1991), 1315–1330 | Zbl

[9] Clarke F.H., Ledyaev Yu.S., “Mean Value Inequalities in Hilbert Space”, Trans. Amer. Math. Society, 344:1 (1994), 307–324 | DOI | MR | Zbl

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

[11] Wolenski P.R., “Hamilton-Jacobi Theory for Hereditary Control Problems”, Nonlinear Analysis, Theory, Methods and Applications, 22:7 (1994), 875–894 | DOI | MR | Zbl

[12] Aubin J.P., Haddad G., “History Path Dependent Optimal Control and Portfolio Valuation and Management”, Positivity, 6 (2002), 331–358 | DOI | MR | Zbl

[13] Lukoyanov N.Yu., “Differentsialnye neravenstva dlya negladkogo funktsionala tseny v zadachakh upravleniya sistemami s posledeistviem”, Tr. IMM UrO RAN, 12, no. 2, 2006, 108–118

[14] Lukoyanov N.Yu., Funktsionalnye uravneniya Gamiltona-Yakobi i zadachi upravleniya s nasledstvennoi informatsiei, UrFU, Ekaterinburg, 2011

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