Modified Brachistochrone problem with state constraints and thrust

Recieved: 06/26/2023

Accepted: 08/09/2023

Published: 11/28/2023

Keywords: brachistochrone, phase constraints, Pontryagin’s maximum principle, boundary value problem, optimal trajectory

To cite this article

Smirnova N.V. Modified Brachistochrone problem with state constraints and thrust. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 4, p.54-60 https://doi.org/10.55959/MSU/0137–0782–15–2023–47–4–54–60.

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

Smirnova N.V. (Lomonosov Moscow State University (MSU))

Abstract

The problem of maximizing the horizontal coordinate of a point mass moving in a vertical plane under the influence of gravity, viscous friction, curve reaction force and thrust is considered. It is assumed that state constraints are imposed on the trajectory inclination angle. The system of equations belongs to a certain type, which allows us to reduce the optimal control problem with constraints on the phase variable to the optimal control problem with control constraints. The sequence and number of inclusions of phase constraints in the optimal trajectory and synthesis of optimal control are determined.