About continuity of optimal time, as the function of initial state, for linear control objects

Recieved: 01/11/2022

Accepted: 03/25/2023

Published: 05/31/2023

Keywords: optimal time control, measured control functions, Cauchy formula, set-valued maps, integration

To cite this article

Nikolskii M.S. About continuity of optimal time, as the function of initial state, for linear control objects. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 2, p.31-38 https://doi.org/10.55959/MSU/0137–0782–15–2023–47–2–31–38.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Nikolskii M.S. (Lomonosov Moscow State University (MSU))
(Steklov Mathematical Institute of the Russian Academy of Sciences)

Abstract

It is considered the question about continuity of optimal time, as the function of initial state, for linear control objects. We obtained some generalization of the Theorems 21, 22 from the second Chapter of monograph E.B.Lee, L.Markus “Foundations of Optimal Control Theory,” J.Wiley and Sons, 1967, connected with continuity of optimal time, as the function of initial state, for linear controlled objects. In the article we broadly use the apparatus of support functions from Convex Analysis. Our results are obtained in more constructive form than another general results In this direction. In the first part we consider stationary case and in the second part it is considered non-stationary case.