Perturbations of Time Optimal Control Problems for a Class of Abstract Parabolic Systems
Perturbations of Time Optimal Control Problems for a Class of Abstract Parabolic Systems
复制标题
DOI：
10.1137/15m101909x
复制
发表时间：
2015-02
期刊：
影响因子：
--
通讯作者：
M. Tucsnak;Gensgsheng Wang;Chi-Ting Wu
中科院分区：
文献类型：
--
作者：
M. Tucsnak;Gensgsheng Wang;Chi-Ting Wu
本文研究了一类抽象抛物型时间最优控制问题的解在生成元在适当意义下收敛于给定的严格负算子时的渐近性态。我们的主要应用程序的偏微分方程系统关注的行为的最优时间和相关的最优控制的抛物方程的高振荡系数，因为我们遇到的均匀化理论。我们的主要结果是，假设目标是一个以原点为中心的正半径闭球，则具有振荡系数的系统的时间最优控制问题的解在通常的范数下收敛于齐次化系统的相应问题的解.为了证明我们的主要定理，我们提供了几个新的结果，这可能是一个更广泛的兴趣，时间和范数最优控制问题。
In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application to PDEs systems concerns the behavior of optimal time and of the associated optimal controls for parabolic equations with highly oscillating coefficients, as we encounter in homogenization theory. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the solutions of the time optimal control problems for the systems with oscillating coefficients converge, in the usual norms, to the solution of the corresponding problem for the homogenized system. In order to prove our main theorem, we provide several new results, which could be of a broader interest, on time and norm optimal control problems.