Аннотация:A terminal control problem with linear dynamics on a fixed time interval and a moving right end of a state trajectory is considered. The convergence of the proposed method is proved for all components of the optimal control problem. Namely, convergence in controls is weak, convergence in state, conjugate trajectories and in terminal variables is strong. The limiting state trajectory at the discretization points passes through all the constraints (sections) of finite-dimensional convex problems.