论文标题
仿射最佳控制问题的稳定性受半椭圆形偏微分方程约束的稳定性
Stability in affine optimal control problems constrained by semilinear elliptic partial differential equations
论文作者
论文摘要
本文研究了仿射最佳控制问题的稳定性，这些问题受半椭圆形偏微分方程约束的限制。这是通过研究与一阶必要最佳条件系统相关的设置值映射的所谓度量次数来完成的。建立了有关涉及功能的不同性能的初步结果，尤其是所谓的切换函数。使用此ANSATZ，比文献中有关控制受约束的椭圆问题的文献中先前考虑的更通用的非线性扰动被包含在弱的假设下。最后，对结果的适用性进行了说明，并对Tikhonov正则化的一些错误估计值进行了说明。
This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping associated with the system of first order necessary optimality conditions. Preliminary results concerning the differentiability of the functions involved are established, especially the so-called switching function. Using this ansatz, more general nonlinear perturbations are encompassed, and under weaker assumptions, than the ones previously considered in the literature on control constrained elliptic problems. Finally, the applicability of the results is illustrated with some error estimates for the Tikhonov regularization.
