This article is cited in 3 papers

Dynamic systems and optimal control

Parametric regularization of a linear-quadratic problem on a set of piecewise linear controls

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

a</sup> Irkutsk State University, Irkutsk, Russian Federation
^b Baikal State University, Irkutsk, Russian Federation

Abstract: A linear-quadratic problem with arbitrary matrices in the functional and multidimensional control with convex constraint is considered. Acceptable controls are piecewise linear vector functions within an uneven grid of possible corner points. The reduction of the optimal control problem into a finite-dimensional format is carried out using vector formalization of the linear spline construction and block matrices together with the corresponding operations. The possibility of influencing the functional in the original problem is provided by using parameters with quadratic forms. The choice of these parameters is focused on the regularization of the functional in the sense of providing it with the properties of convexity or concavity at the level of a finite-dimensional model. The conditions for the choice of parameters are in the nature of inequalities with respect to the extreme eigenvalues of the block matrices forming the objective function. The corresponding convex or concave optimization problems can be solved in a finite number of iterations.

Keywords: linear-quadratic problem, multidimensional piecewise linear control, functional with parameters, regularization of the problem.

UDC: 517.977

MSC: 49J15, 49M25

Received: 29.06.2022
Revised: 05.08.2022
Accepted: 15.08.2022

DOI: 10.26516/1997-7670.2022.41.57

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