ИСТИНА

In this talk, a problem of terminal control with linear dynamics on a finite time interval is considered. The right-hand end of the trajectory is defined implicitly as a solution of boundary-value problem. A finite-dimensional optimization problem for sensitivity function under constraints acts as a boundary-value problem. Sensitivity function is generated by the parameter, which is a right-hand part of the functional constraints in the convex programming problem. This parameter is a variable for the sensitivity function. Properties of this function were studied in the paper. To solve the problem of terminal control with implicitly given boundary-value condition, we use an approach based on reducing the problem to finding a saddle point of the Lagrange function. Linear dynamics is regarded as a restriction of equality type. In the convex case, both components of the saddle point form the primal and dual solutions of the original dynamic system. Both components satisfy the saddle-point inequalities. The inequality in primal variables plays the role of the Pontryagin maximum principle. Together with the inequality in dual variables this saddle-point system can be considered as a strengthening of the maximum principle. The proposed approach allows us to construct new iterative methods for solving the saddle-point type problems and prove their convergence to problem solution in all components.