Abstract

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.

中文翻译：

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非局部连续性方程博弈论控制问题中的反馈策略

摘要

本文讨论连续性方程的博弈论控制问题。假设多智能体系统的所有智能体都受到两个玩家的相同控制的影响，仅取决于当前时间和智能体的当前分布。我们将\(u\) -和\(v\)-稳定性和Krasovskii-Subbotin极值转移规则的概念扩展到给定的情况，并构建参与者的次优策略。此外，还证明了价值函数的存在定理。