Abstract

The paper deals with the construction of universal closed-loop strategies for two-person nonzero-sum differential game of a special type. The dynamics of the first player is defined by its own position and control. The dynamics of the second player is defined by its own control and the position of both players. The strategies are constructed based on the solution of a system of Hamilton–Jacobi equations. The system of Hamilton–Jacobi equations has a hierarchical type. A generalized solution of the system of Hamilton–Jacobi equations belongs to the class of multivalued mappings. We show the relationship between the values of the players and the generalized solution of the system of Hamilton–Jacobi equations.

中文翻译：

---

特殊类型非零和微分博弈中的反馈策略

摘要

本文讨论了特殊类型的两人非零和微分博弈的通用闭环策略的构建。第一个球员的动态是由他自己的位置和控制来定义的。第二名球员的动态由他自己的控制和两名球员的位置决定。这些策略是基于 Hamilton-Jacobi 方程组的解而构建的。Hamilton-Jacobi 方程组具有层次类型。Hamilton-Jacobi 方程组的广义解属于多值映射类。我们展示了参与者的价值与 Hamilton-Jacobi 方程组的广义解之间的关系。