Variational Integrators for a new Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term
Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martin de Almagro R (2025)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2025
Journal
Book Volume: 36
Article Number: 11
DOI: doi.org/10.1007/s00332-025-10229-5
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. As an example, a family of low-order integration schemes is devised to find approximate optimality conditions, which are used to solve both a low-thrust orbital transfer and satellite alignment problem, including a convergence and performance study. Non-trivial equivalent standard direct methods are constructed. Noether’s theorem and symplecticity for the new Lagrangian approach are investigated in the exact and approximate cases.
Authors with CRIS profile
Michael Konopik
Institute of Applied Dynamics
Sigrid Leyendecker
Institute of Applied Dynamics
Rodrigo Sato Martin de Almagro
Institute of Applied Dynamics
Involved external institutions
Germany (DE)How to cite
APA:
Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., & Sato Martin de Almagro, R. (2025). Variational Integrators for a new Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term. Journal of Nonlinear Science, 36. https://doi.org/doi.org/10.1007/s00332-025-10229-5
MLA:
Konopik, Michael, et al. "Variational Integrators for a new Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term." Journal of Nonlinear Science 36 (2025).
BibTeX: Download