Controllability Problems for the Non-Homogeneous String that is Fixed at the Right End Point and has the Dirichlet Boundary Control at the Left End Point

Abstract

In the paper, the necessary and su±cient conditions of null-controllability and approximate null-controllability are obtained for the some control system. The problems for the control system are considered in the modified Sobolev spaces. The control that solves these problems is found explicitly. The bang-bang controls solving the approximate null-controllability problem are constructed as the solutions of the Markov trigonometric moment problem.