• search hit 7 of 379
Back to Result List

Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal Control

Submission Status:under review
  • It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint variables. High accuracy with moderate computing time can be achieved by such time integration methods that satisfy a sufficiently large number of adjoint order conditions and supply gradients with higher orders of consistency. In this paper, we upgrade our former implicit two-step Peer triplets constructed in [Algorithms, 15:310, 2022] to meet those new requirements. Since Peer methods use several stages of the same high stage order, a decisive advantage is their lack of order reduction as for semi-discretized PDE problems with boundary control. Additional order conditions for the control and certain positivity requirements now intensify the demands on the Peer triplet. We discuss the construction of 4-stage methods with order pairs (4,3) and (3,3) in detail and provide three Peer triplets of practical interest. We prove convergence for s-stage methods, for instance, order s for the state variables even if the adjoint method and the control satisfy the conditions for order s-1, only. Numerical tests show the expected order of convergence for the new Peer triplets.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Jens Lang, Bernhard A. Schmitt
Document Type:Preprint
Language:English
Date of Publication (online):2024/03/21
Release Date:2024/03/21
Volume:http://arxiv.org/abs/2303.18180
Institutes:Technische Universität Darmstadt
Subprojects:B01
Licence (German):License LogoCreative Commons - CC0 1.0 - Universell - Public Domain Dedication