论文标题
关于抛物线最佳控制问题的溶液稳定性
On the solution stability of parabolic optimal control problems
论文作者
论文摘要
本文研究了半连接抛物线偏微分方程的最佳控制问题解决方案的稳定性。对于方程和客观功能相对于对照而言，获得了最佳解决方案对扰动的最佳溶液对扰动的依赖性。扰动可能会出现在方程式和目标函数中，并且可能非线性取决于状态和控制变量。主要结果是基于对目标功能的第一和第二变化的联合生长的最近提出的假设的扩展。最佳解决方案的稳定性是由于本文中获得的更一般结果而获得的 - 证明是与一阶必要最佳条件系统相关的映射的映射的度量次级。此属性还可以实现近似方法的错误估计。 Lipschitz估计最佳控制对Tikhonov正则化参数的依赖性作为副产品获得。
The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. Hölder or Lipschitz dependence of the optimal solution on perturbations are obtained for problems in which the equation and the objective functional are affine with respect to the control. The perturbations may appear in both the equation and in the objective functional and may non-linearly depend on the state and control variables. The main results are based on an extension of recently introduced assumptions on the joint growth of the first and second variation of the objective functional. The stability of the optimal solution is obtained as a consequence of a more general result obtained in the paper -- the proved metric subregularity of the mapping associated with the system of first-order necessary optimality conditions. This property also enables error estimates for approximation methods. Lipschitz estimate for the dependence of the optimal control on the Tikhonov regularization parameter is obtained as a by-product.
