Effective Content of the Calculus of Variations I: Semi-Continuity and the Chattering Lemma
Effective Content of the Calculus of Variations I: Semi-Continuity and the Chattering Lemma
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变分微积分的有效内容一：半连续性和颤振引理
DOI：
10.1016/0168-0072(95)00034-8
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
A. Nerode
中科院分区：
文献类型：
--
作者：
Xiaolin Ge;A. Nerode
对变分中存在定理的内容进行了探讨，得到了半连续性的一种有效处理方法。已发展出一种算法，该算法捕捉了半连续函数概念的自然算法内容，并用于获得控制论和常微分方程组中的“颤振引理”的有效版本。这一引理揭示了松弛最优控制理论的主要计算内容。
The content of existence theorems in the calculus of variations has been explored and an effective treatment of semi-continuity has been achieved. An algorithm has been developed which captures the natural algorithmic content of the notion of a semi-continuous function and this is used to obtain an effective version of the “chattering lemma” of control theory and ordinary differential equations. This lemma reveals the main computational content of the theory of relaxed optimal control.