On the Existence of Time Optimal Controls with Constraints of the Rectangular Type for Heat Equations
On the Existence of Time Optimal Controls with Constraints of the Rectangular Type for Heat Equations
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DOI：
10.1137/10081277x
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发表时间：
2011-05
期刊：
影响因子：
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通讯作者：
Qi Lü;GengshengBB Wang
中科院分区：
文献类型：
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作者：
Qi Lü;GengshengBB Wang
本文针对内控热方程提出了一类具有矩形控制约束的时间最优控制问题。建立了这类问题的时间最优控制的存在性结果。矩形控制约束源于对常微分方程组时间最优控制问题的研究。在有限维情形下，从最优控制的存在性研究的角度来看，这类具有矩形和球型控制约束的问题没有区别。有趣的是，在无限维的情况下，具有矩形类型的控制约束的问题与具有球型控制约束的问题本质上不同。对于无限维系统，具有球型约束的时间最优控制的存在性已经在文献中得到了讨论，而对矩形约束的研究就我们所知还没有涉及。
This paper presents a time optimal control problem with control constraints of the rectangular type for internally controlled heat equations. An existence result of time optimal controls for such a problem is established. The rectangular type of control constraints originates from the study of time optimal control problems for ordinary differential equations. In the finite dimensional case, there is no difference between such problems with control constraints of the rectangular type and those of the ball type, from the perspective of the study on the existence of optimal controls. Interestingly, in the infinite dimensional case, the problem with control constraints of the rectangular type differs essentially from that with control constraints of the ball type. For infinite dimensional systems, the existence for time optimal controls with constraints of the ball type has already been discussed in the literature, while the study of the rectangular type has not been touched upon as far as we know.