The interconnection between an optimal control problem and its convexification in the sense of Gamkrelidze and Bogolyubov is studied. Bogolyubov’s classical result for the simplest problem of variational calculus is obtained as a corollary.

中文翻译：

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Gamkrelidze 凸化和 Bogolyubov 定理

研究了 Gamkrelidze 和 Bogolyubov 意义上的最优控制问题与其凸化之间的相互联系。Bogolyubov 对最简单的变分微积分问题的经典结果是作为推论获得的。