Methods of boundary-value problems for improving control in systems with constraints

D. O. Trunin

Buryat State University, Ulan-Ude

Abstract: In the class of state-nonlinear optimal control problems with constraints, a new approach to improving controls is proposed. This approach is based on solving special boundary-value problems by perturbation methods and parametrization of the optimal control problem by the perturbation parameter. The solution of the constructed unperturbed boundary-value problem is reduced to the solution of an algebraic equation for one unknown parameter. To solve the perturbed boundary-value problem, an iterative process is proposed, at each iteration of which a problem is solved that is similar in complexity to the unperturbed problem.

Keywords: controlled system with constraints, boundary-value problem of control improvement, perturbation method, iterative algorithms

UDC: 517.977

MSC: 49M20

DOI: 10.36535/2782-4438-2025-239-43-52

 English version: Journal of Mathematical Sciences (New York), 2025, 292:3, 373–382