Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term
Abstract
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact discrete and semi-discrete versions of the problem, providing new tools to develop numerical methods. Discrete necessary conditions for optimality are derived and their equivalence with the continuous version is proven. A family of low-order integration schemes is devised to find approximate optimality conditions, and used to solve a low-thrust orbital transfer problem. Non-trivial equivalent standard direct methods are constructed. Noether's theorem for the new Lagrangian approach is investigated in the exact and approximate cases.
Keywords
Cite
@article{arxiv.2502.04742,
title = {Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term},
author = {Michael Konopik and Rodrigo T. Sato Martín de Almagro and Sofya Maslovskaya and Sina Ober-Blöbaum and Sigrid Leyendecker},
journal= {arXiv preprint arXiv:2502.04742},
year = {2025}
}