On the Optimal Control of a Linear Peridynamics Model

We study a non-local optimal control problem involving a linear, bond-based peridy-namics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter d, 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 d tend to zero simultaneously.