Discrete adjoint method for variational integration of constrained ODEs and its application to optimal control of geometrically exact beam dynamics

Matthias Schubert, Rodrigo T. Sato Martin de Almagro, Karin Nachbagauer, Sina Ober-Blöbaum, Sigrid Leyendecker

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

Abstract

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal solution. While the benefits of structure preserving or geometric methods have been known for decades, their exploration in the context of optimal control problems is a relatively recent field of research. In this work, the discrete adjoint method is derived for variational integrators yielding structure preserving approximations of the dynamics firstly in the ODE case and secondly for the case in which the dynamics is subject to holonomic constraints. The convergence rates are illustrated by numerical examples. Thirdly, the discrete adjoint method is applied to geometrically exact beam dynamics, represented by a holonomically constrained PDE.

OriginalspracheEnglisch
Seiten (von - bis)447-474
Seitenumfang28
FachzeitschriftMultibody System Dynamics
Jahrgang60
Ausgabenummer3
Frühes Online-Datum2023
DOIs
PublikationsstatusVeröffentlicht - März 2024

Schlagwörter

  • Holonomically constrained system
  • Optimal control
  • Discrete adjoint method
  • Variational integrators
  • Geometrically exact beam

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