Construction of the controllability set for one second-order system with different positive eigenvalues and with a state constraint

Recieved: 04/19/2024

Accepted: 12/25/2024

Published: 06/20/2025

Keywords: time optimal control, state constraint, linear system, controllability set

To cite this article

Goncharova M.N., Samsonov S.P. Construction of the controllability set for one second-order system with different positive eigenvalues and with a state constraint. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2025. N 2, p.15-29 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–2–15–29.

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

Goncharova M.N. (Yanka Kupala Grodno State University)
Samsonov S.P. (Lomonosov Moscow State University (MSU))

Abstract

Time optimal control problem with state constraint investigated in this article. The behavior of an object is described by a system of second-order linear differential equations. The coefficient matrix for state variables has various positive eigenvalues. The state constraint is linear. A admissible control is a piecewise continuous function that takes values from a given compact set. Sets of controllability to the origin are constructed for time intervals of various lengths. A study of the dependence of the solution of the problem on the parameter determining the state constraint was carried out.