发表机构
Universidad de Santiago de Chile; University of Tübingen（智利圣地亚哥大学; 蒂宾根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无Tikhonov正则化、受半线性椭圆方程约束的盒约束分布式最优控制问题，提出定量条件以保证二阶条件在状态与跟踪数据扰动下的稳定性。
AI 中文摘要
本文研究受半线性椭圆方程约束、带盒约束的分布式最优控制问题的定量最优性条件，该类最优控制问题无Tikhonov正则化这一重要性质。已知在给定控制下，二阶变分是线性化状态的二次型，其曲率系数函数可能消失或变号。本文提出一种定量条件，该条件蕴含线性化状态关于L²范数的强制性，由此证明二阶条件在状态与跟踪数据扰动下的稳定性。
英文摘要
In this paper, a general principle for coercivity in optimal control problems is investigated. Utilizing regularity properties of solutions to second-order elliptic PDEs on Lipschitz domains, we provide quantitative sufficient second-order optimality condition for control-constrained semilinear elliptic optimal control problems. The main property of the investigated optimal control problems is the absence of a Tikhonov regularization term on the objective function. For these problems, the second variation is a quadratic form in the linearized state, and its curvature function may vanish or change sign. The quantitative condition we introduce implies coercivity with respect to the $L^2$-norm of the linearized-states. As a consequence, the stability of the sufficient second-order condition under perturbations of the states and the tracking data is shown.
