On a certain procedure of non-local improvement of controls in quadric-in-state systems with terminal restrictions

In the article we propose an approach to nonlocal improvement of controls in the class of quadratic-in-state and linear problems of optimal control with a partially fixed right end based on the solution of a system of functional equations in the space of controls that determines the conditions for nonlocal management improvement. To solve the system under consideration we use an iterative process, and the scalar equation is solved at each iteration. The procedure ensures the improvement of permissible control without variation and with preservation of all terminal constraints and is used for solving a constrained problem using an iterative. Comparative efficiency of the method is illustrated on the model problem.