ИСТИНА

A new approach to solving terminal control problems with phase constraints, based on saddle-point sufficient optimality conditions, is considered. The basis of the approach is Lagrangian formalism and duality theory. We study linear controlled dynamics in the presence of phase constraints. The cross section of phase constraints at certain points in time leads to the appearance of new intermediate finite-dimensional convex programming problems. In fact, the optimal control problem, defined over the entire time interval, is split into a number of independent intermediate subproblems, each of which is defined in its own sub-segment. Combining the solutions of these subproblems together, we can obtain solutions to the original problem on the entire time interval. To this end, a gradient flow is launched to solve all intermediate problems at the same time. The convergence of computing technology to the solution of the optimal control problem in all variables is proved.