Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term
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arXiv
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| Format: | Preprint |
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2025
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| author | Konopik, Michael de Almagro, Rodrigo T. Sato Martín Maslovskaya, Sofya Ober-Blöbaum, Sina Leyendecker, Sigrid |
| author_facet | Konopik, Michael de Almagro, Rodrigo T. Sato Martín Maslovskaya, Sofya Ober-Blöbaum, Sina Leyendecker, Sigrid |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term Konopik, Michael de Almagro, Rodrigo T. Sato Martín Maslovskaya, Sofya Ober-Blöbaum, Sina Leyendecker, Sigrid Optimization and Control 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. |
| title | Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.04742 |