In this paper, we consider parametric optimal control problems with linear state equations and control constraints. Applying the KKM fixed point theorem and the Gronwall Lemma, conditions of the existence of solutions to such problems are gained. Under suitable tools and techniques, we formulate sufficient conditions of a Hölder property of solution maps to reference problems without assuming conditions related to differentiability properties. Also, we suggest and investigate a concept of Hölder well-posedness for these problems. Finally, as applications, employing the main results, we discuss the Hölder calmness property of the solution maps to two practical situations, namely linear quadratic regulator and fuel-optimal frictionless horizontal motion of a mass point problems.

在本文中，我们考虑了具有线性状态方程和控制约束的参数最优控制问题。应用 KKM 不动点定理和 Gronwall 引理，获得了此类问题的解存在的条件。在合适的工具和技术下，我们制定解映射的 Hölder 属性的充分条件来参考问题，而不假设与可微性属性相关的条件。此外，我们针对这些问题提出并研究了 Hölder 适定性的概念。最后，作为应用，采用主要结果，我们讨论了解决方案映射到两种实际情况的Hölder平静特性，即线性二次调节器和质点的燃料最优无摩擦水平运动问题。