2025/02/07 by Michael Konopik, Konopik, Michael, Rodrigo T. Sato Martín de Almagro +6 · 1 citation
Mathematics · Engineering · #Numerical methods for differential equations #Differential Equations and Numerical Methods #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.2502.04742
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.