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. 
@article{DANMA_2020_490_a20,
     author = {N. Yu. Lukoyanov and A. R. Plaksin},
     title = {Inequalities for subgradients of a value functional in differential games for time-delay systems},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {91--94},
     publisher = {mathdoc},
     volume = {490},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_490_a20/}
}
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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/