Presymplectic integrators for optimal control problems via retraction maps

2022/03/01 by María Barbero-Liñán, David Martı́n de Diego, Liñán, María Barbero +1
Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2203.00790

openalex publication_date 2022/03/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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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