An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems
An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems
复制标题
一类无限时域最优控制问题的存在定理
DOI：
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发表时间：
2016
影响因子：
1.9
通讯作者：
Valeriya Lykina
中科院分区：
文献类型：
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作者：
Valeriya Lykina
在本文中，我们处理涉及仿射线性动力学的无限范围最优控制问题，并证明最优解的存在性。本文的创新之处在于问题的特殊设置，恰恰在于选择加权索博列夫空间和加权勒贝格空间分别作为状态空间和控制空间，这对于各种问题都是有意义的。我们应用广义Weierstraß定理来证明存在性结果。在弱化假设下显示了所需的下半连续定理。
In this paper, we deal with infinite horizon optimal control problems involving affine-linear dynamics and prove the existence of optimal solutions. The innovation of this paper lies in the special setting of the problem, precisely in the choice of weighted Sobolev and weighted Lebesgue spaces as the state and control spaces, respectively, which turns out to be meaningful for various problems. We apply the generalized Weierstraß theorem to prove the existence result. A lower semicontinuity theorem which is needed for that is shown under weakened assumptions.