The introduction of “cheap” controls for minimizing the simplest energy functional in an optimal control problem related to the reconstruction of a defective curve necessitates solving a singularly perturbed variational problem with fixed time and fixed ends. The construction of a uniform zero asymptotic approximation to the optimal control in the latter problem permits one to conclude that the optimal trajectories in the original optimal control problem combine a uniform motion in the interior of the time interval with rapid transition layers at the boundaries of the control interval.
Title: Optimal Control Problem Related to the Reconstruction of a Defective Curve
Authors: M.G. Dmitriev, Yu.L. Sachkov
Journal title: Differential Equations