具有超线性-次临界控制的分数阶最优控制问题解的存在性
Existence of Solutions for Fractional Optimal Control Problems with Superlinear-subcritical Controls
AI总结：
本文研究基于一般分数阶核的椭圆最优控制问题，在满足增长界限和超线性-次临界条件下，构造容许控制集并应用山路定理，证明了解的存在性，并探讨了理论的局限性与局部情形。
摘要：
本文给出了基于一般分数阶核的椭圆最优控制问题解的存在性结果，其中容许控制来自同时满足增长界限和超线性-次临界条件的类。已知每个容许控制通过将山路定理应用于分数阶方程，产生非平凡的对应状态。主要理论贡献是构造了一个合适的容许控制集，在其上可调整具有线性和半线性状态约束的控制问题的标准存在性理论。本文特别解释了这类控制问题中出现的新困难，以论证该理论的局限性。为完整起见，还研究了相应的局部椭圆控制问题。
英文摘要：
This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class satisfying both a growth bound and a superlinear-subcritical condition. Each admissible control is known to produce a nontrivial corresponding state by applying the Mountain Pass Theorem to fractional equations. The main theoretical contribution is the construction of a suitable set of admissible controls on which the the standard existence theory for control problems with linear and semi-linear state constraints can be adapted. Extra care is taken to explain what new difficulties arise for these types of control problems, to justify the limitations of this theory. For completeness, the corresponding local elliptic control problem is also studied.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
