In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We firstly introduce suitable hypotheses to prove the existence and uniqueness of mild solutions for this kind of Riemann-Liouville fractional evolution equations with history-dependent operators. Then, by introducing a feedback iterative technique and applying Filippov theorem, we show the existence of feasible pairs and optimal control pairs of the optimal feedback control systems with history-dependent operators. Finally, we give some applications to illustrate our main results.

在本文中，我们将研究在可分离的自反巴拿赫空间中由一类具有历史相关算子的黎曼-刘维尔分数演化方程导出的最优反馈控制问题。我们首先引入合适的假设来证明这种具有历史相关算子的 Riemann-Liouville 分数阶演化方程的温和解的存在性和唯一性。然后，通过引入反馈迭代技术并应用 Filippov 定理，我们证明了具有历史相关算子的最优反馈控制系统的可行对和最优控制对的存在。最后，我们给出一些应用来说明我们的主要结果。