Parametric transformation of nonconvex optimal control problems

V. A. Srochko^a, E. V. Aksenyushkina<sup>b

a</sup> Irkutsk State University
^b Baikal State University

Abstract: A nonconvex linear-quadratic optimal control problem with indefinite matrices of quadratic forms is considered. The transformation and parametrization of the target functional are performed; this leads to a family of identical problems in the sense of a global solution. Conditions on the parameters that distinguish convex problems are obtained. A parametric optimization procedure is implemented according to the criterion of proximity to the original problem. As a result, convex linear-quadratic problems are constructed, which provide the possibility of improving extremal controls in a nonconvex problem.

Keywords: linear-quadratic problem, transformation and parameterization of functional, convex problems, improvement of extremal controls

UDC: 517.977

MSC: 49J15, 49M25

DOI: 10.36535/2782-4438-2025-241-64-70