Geodesic
Feedback Strategies in a Game-Theoretical Control Problem for a Nonlocal Continuity Equation
Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 525-542

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The paper deals with game-theoretical control problem for the continuity equation. It is assumed that all agents of a multiagent system are influenced by the same controls of both players depending only on current time and current distribution of the agents. We extend the notion of $u$- and $v$-stability and the Krasovskii–Subbotin extremal shift rule to a given case and construct suboptimal strategies of players. Also, the existence theorem for a value function is proved.
Keywords: feedback control, differential game, nonlocal continuity equation, extremal shift rule. 
@article{MZM_2023_114_4_a3,
     author = {E. A. Kolpakova},
     title = {Feedback {Strategies} in a {Game-Theoretical} {Control} {Problem} for a {Nonlocal} {Continuity} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {525--542},
     publisher = {mathdoc},
     volume = {114},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a3/}
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E. A. Kolpakova. Feedback Strategies in a Game-Theoretical Control Problem for a Nonlocal Continuity Equation. Matematičeskie zametki, Tome 114 (2023) no. 4, pp. 525-542. http://geodesic.mathdoc.fr/item/MZM_2023_114_4_a3/