论文标题
伴随的间隔收费公路属性
The interval turnpike property for adjoints
论文作者
论文摘要
在这项工作中，我们得出了一个间隔收费公路结果，该结果是在状态和控件上的间隔收费公路下的有限和无限二维非线性最佳控制问题的伴随。我们考虑由具有有限维的不稳定部分的半群的发电机控制的可稳定动力学，满足光谱分解条件，并在一阶最佳条件下显示在连续性假设下所需的收费公路属性。我们进一步给出了分析性半群的更强估计，并提供了一个数值示例，具有边界控制的半线性热方程式以说明结果。
In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger estimates for analytic semigroups and provide a numerical example with a boundary controlled semilinear heat equation to illustrate the results.
