About one approach to nonlocal control improvement in quadratic-in-the-state systems with terminal constraints

In the article we propose an approach to nonlocal improvement of admissible controls in quadratic-in-the-state optimal control problems with a partially fixed right end based on solution of a system of functional equations, that determine the conditions for nonlocal improvement. For solving the system under consideration, the perturbation method have been used, grounded in separation of nonlinear part that is linear in the state and parametrization of nonlinear part by the perturbation parameter. The solution of the unperturbed problem reduces to solution of an algebraic equation. To solve the perturbed problem, an iterative process is constructed, at each iteration a problem similar to the unperturbed one is solved.