论文标题
来源中的本地和非局部最佳控制
Local and nonlocal optimal control in the source
论文作者
论文摘要
分析了非局部类型的最佳控制问题的分析。获得的结果应用于研究相应的局部最佳控制问题。状态方程由局部和非局部类型的p-Laplacian椭圆运算符约束，成本属于一类广泛的积分功能。非局部问题是通过国家用内核的卷积提出的。该内核取决于一个称为Horizon的参数，该参数负责方程的非局部性。输入函数是椭圆方程的来源。获得了非局部控制的存在，并在此任务中采用了G-连接结果。分析地平线倾向于零时，非局部最佳对照的溶液的限制进行分析，并将其与基础局部最佳控制问题的溶液进行比较。
The analysis of an optimal control problem of nonlocal type is analyzed. The results obtained are applied to the study the corresponding local optimal control problems. The state equations are governed by p-laplacian elliptic operators, of local and nonlocal type, and the costs belong to a wide class of integral functionals. The nonlocal problem is formulated by means of a convolution of the states with a kernel. This kernel depends on a parameter, called horizon which, is responsible for the nonlocality of the equation. The input function is the source of the elliptic equation. Existence of nonlocal controls is obtained and a G-convergence result is employed in this task. The limit of the solutions of the nonlocal optimal control, when the horizon tends to zero, is analyzed and compared to the solution of the underlying local optimal control problem.
