最优控制问题的松弛方法

IF 1.1 2区数学 Q1 MATHEMATICS

Bulletin of Mathematical Sciences Pub Date : 2020-02-25 DOI:10.1142/S1664360720500046

N. Papageorgiou, Vicentiu D. Rădulescu, Dušan D. Repovš

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引用次数: 8

摘要

我们考虑一个非线性最优控制问题，其动力学由一个包含极大单调映射的微分包含所描述[公式:见文本]。我们不假设[公式:见文本]，以这种方式将具有单边约束的系统纳入我们的框架。我们提出了两种松弛方法。第一种方法是存在理论的约简方法的产物，而第二种方法使用杨测度。我们证明了这两种松弛方法是等价的和可接受的。

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Relaxation methods for optimal control problems

We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map [Formula: see text]. We do not assume that [Formula: see text], incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.

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来源期刊

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.