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arXiv · 2502.04742

Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term

Michael Konopik·Rodrigo T. Sato Martín de Almagro·Sofya Maslovskaya·Sina Ober-Blöbaum·Sigrid Leyendecker
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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.

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Michael Konopik, Rodrigo T. Sato Martín de Almagro, Sofya Maslovskaya, Sina Ober-Blöbaum, Sigrid Leyendecker. 2025-02-07. Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term. https://arxiv.org/abs/2502.04742

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