ИСТИНА

A problem of terminal control on a fixed time interval is considered. In the interval, a linear controlled dynamics develops. By choosing a control, the system of differential equations generates a phase trajectory that describes some dynamic process. Discretization of the time interval is carried out, when the initial interval is divided into n subintervals. Sections of the phase trajectory at discretization points are considered. In the finite-dimensional spaces corresponding to these points, linear programming problems are additionally formulated, and the values of the phase trajectory at discretization points must be the solutions of these problems. In the problem, it is required to choose a control from some convex closed set so that the phase trajectory corresponding to this control passes through the optimal solutions of all linear programming problems. This problem is interpreted as a mathematical model for control a multi-agent system that is controlled from a single center. In the model, the connections between agents represented by linear programming problems (for example, matrix connections) are not yet available, but they can easily be taken into account in this rather flexible system. The model belongs to complex optimal control problems. In the paper, gradient saddle-point methods are developed for calculating the solution. The methods are guaranteed to converge to the exact solution of the original problem. The substantiation of convergence was carried out within the framework of evidence-based methodology. The latter means that convergence takes place in all components of the solution, i.e., we have weak convergence in control, and strong convergence in phase and conjugate trajectories, as well as in terminal variables of intermediate problems.