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首页> 外文期刊>International game theory review >VERIFICATION THEOREMS FOR OPTIMAL FEEDBACK STRATEGIES IN DIFFERENTIAL GAMES
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VERIFICATION THEOREMS FOR OPTIMAL FEEDBACK STRATEGIES IN DIFFERENTIAL GAMES

机译：差分游戏最优反馈策略的验证定理

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摘要

We give complete proofs to the verification theorems announced recently by the author for the "pairs of relatively optimal feedback strategies" of an autonomous differential game. These concepts are considered to describe the possibly optimal solutions of a differential game while the corresponding value functions are used as "instruments" for proving the relative optimality and also as "auxiliary characteristics" of the differential game. The 6 verification theorems in the paper are proved under different regularity assumptions accompanied by suitable differential inequalities verified by the generalized derivatives, mainly of contingent type, of the value function.
机译：我们为作者最近宣布的针对自主微分游戏的“成对的相对最优反馈策略”的验证定理提供了完整的证明。这些概念被认为是描述差分博弈的可能最优解，而相应的值函数被用作证明相对最优性的“工具”以及差分博弈的“辅助特性”。本文中的6个验证定理在不同的正则性假设下得到证明，并伴有由价值函数的广义导数（主要是或有类型）证明的适当的微分不等式。

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