Equivalence of Three Different Kinds of Optimal Control Problems for Heat Equations and Its Applications
Equivalence of Three Different Kinds of Optimal Control Problems for Heat Equations and Its Applications
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DOI：
10.1137/110852449
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发表时间：
2011-10
期刊：
影响因子：
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通讯作者：
GengshengBB Wang;Yashan Xu
中科院分区：
文献类型：
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作者：
GengshengBB Wang;Yashan Xu
本文给出了三种不同类型的最优控制问题的等价性定理，它们是最优目标控制问题、最优时间控制问题和最优范数控制问题。本研究中的受控系统是内部控制的热方程。利用这一定理，我们建立了一个最优范数反馈律，并给出了求解最优范数和最优时间控制问题的显式算法。
This paper presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal time control problems, and optimal norm control problems. Controlled systems in this study are internally controlled heat equations. With the aid of this theorem, we establish an optimal norm feedback law and build up some explicit algorithms for solutions of optimal norm and optimal time control problems.