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

Vladimir A. Srochko ; Elena V. Aksenyushkina

The Bulletin of Irkutsk State University. Series Mathematics, Tome 41 (2022), pp. 57-68

Résumé

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.

Détail

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