ИСТИНА

Classical problem of terminal control with linear dynamics and fixed ends of trajectory is considered in a Hilbert space. In contrast to the traditional approach, the problem of terminal control is interpreted not as an optimization problem, but as a saddle-point problem. The solution to this problem is a saddle point of the Lagrange function with components in the form of controls, phase and conjugate trajectories. The problem is a convex programming problem formulated in Hilbert space. The extragradient method of saddle-point type was used. In convex case, saddle-point approach provides the convergence of iterative process to solution of the problem in all components, and could be interpreted as strengthening the Pontryagin maximum principle. The weak convergence of the method in controls, and strong convergence in phase and conjugate trajectories were proved.