ИСТИНА

A method for solving the terminal control problem with discrete phase constraints is proposed. The method is based on the Lagrangian formalism and duality theory, thanks to which it is possible to realize the necessary and sufficient optimality condition for the class of convex problems with linear dynamics. The time interval is divided into a finite number of sub-segments, on each of which, using the technique developed by the authors, the basic problem is solved as a terminal control problem with a boundary-value problem at the right-hand end of the interval. In each such problem, the minimum of the convex objective functional is sought on the set determined by phase constraints (convex polyhedron). As a result, the original problem is broken into a finite number of sub-problems. The peculiarity of the statement of the problem is that all intermediate problems are solved sequentially, and the right end of the trajectory found on each subsegment (as a solution to the finite-dimensional boundary value optimal control problem) serves as the initial value for the phase trajectory in the next time interval. To solve intermediate problems, a saddle-point method of an extragradient type is implemented. The convergence of the method to the solution in all its components is proved: weak convergence in controls, strong convergence in phase and conjugate trajectories, and also in finite-dimensional terminal variables.