Title: Optimal Control Problem Related to the Reconstruction of a Defective Curve

Authors: M.G. Dmitriev, Yu.L. Sachkov

Journal title: Differential Equations

Year: 2013

Issue: 11

Volume: 49

Pages: 1347-1355

Abstract:

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.