We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter $\delta$, which controls the degree of nonlocality, approaches zero. We then study a finite element-based discretization of this problem, its convergence, and the so-called asymptotic compatibility as the discretization parameter $h$ and the horizon parameter $\delta$ tend to zero simultaneously.

翻译：我们研究了一个涉及线性键基近场动力学模型的非局部最优控制问题。除了问题解的存在唯一性外，我们还探究了当控制非局部程度的水平参数$\delta$趋于零时解的行为。随后，我们研究了该问题的基于有限元的离散化方法、其收敛性，以及当离散化参数$h$与水平参数$\delta$同时趋于零时所谓的渐近相容性。