Presymplectic integrators for optimal control problems via retraction maps

María Barbero Liñán; David Martín de Diego

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arXiv · 2203.00790

Presymplectic integrators for optimal control problems via retraction maps

María Barbero Liñán·David Martín de Diego

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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.

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BibTeX RIS

María Barbero Liñán, David Martín de Diego. 2022-03-01. Presymplectic integrators for optimal control problems via retraction maps. https://arxiv.org/abs/2203.00790

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