Tikhonov solutions of approximately controllable second-order semilinear control systems

This manuscript considers a second-order semilinear control system in Hilbert space. By using Tikhonov regularization, we first construct the regularized control for the corresponding linear system and prove its approximate controllability. We then establish approximate controllability results using Gronwall's Lemma for the semilinear system. In addition, the error estimates and convergence rates involved in the regularization procedure are also obtained. Further, we give an example to demonstrate the results.