ИСТИНА

A new approach to solving terminal control problems with phase constraints, based on sufficient optimality conditions, is considered. The basis of the approach is Lagrangian formalism and duality theory. Under linear controlled dynamics, the cross section of phase constraints at certain points in time leads to the appearance of intermediate optimal control problems without phase constraints. On each interval between two points of the cross section, a full-fledged intermediate optimal control problem is formed with a fixed left and moving right end of the phase trajectory. The solution of each intermediate problem serves as an initial condition for the next intermediate problem. To solve problems, a saddle-point method of an extragradient type is proposed. The convergence of the method to the solution of the problem in all variables is proved.