Presymplectic integrators for optimal control problems via retraction maps
Optimization and Control
2022-03-03 v1 Numerical Analysis
Numerical Analysis
Symplectic Geometry
Abstract
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the cotangent bundle so that symplectic integrators are constructed for Hamilton's equations. Optimal control problems are provided with a Hamiltonian framework by Pontryagin's Maximum Principle. That is why we use discretization maps and the integrability algorithm to obtain presymplectic integrators for optimal control problems.
Cite
@article{arxiv.2203.00790,
title = {Presymplectic integrators for optimal control problems via retraction maps},
author = {María Barbero Liñán and David Martín de Diego},
journal= {arXiv preprint arXiv:2203.00790},
year = {2022}
}