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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)447-474
Number of pages28
JournalMultibody System Dynamics
Volume60
Issue number3
Early online date2023
DOIs
Publication statusPublished - Mar 2024

Keywords

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

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