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Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems

Lang, Jens ; Schmitt, Bernhard A. (2022)
Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems.
In: Algorithms, 2022, 15 (9)
doi: 10.26083/tuprints-00022452
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Item Type: Article
Type of entry: Secondary publication
Title: Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems
Language: English
Date: 10 October 2022
Place of Publication: Darmstadt
Year of primary publication: 2022
Publisher: MDPI
Journal or Publication Title: Algorithms
Volume of the journal: 15
Issue Number: 9
Collation: 30 Seiten
DOI: 10.26083/tuprints-00022452
Corresponding Links:
Origin: Secondary publication DeepGreen

This paper is concerned with the construction and convergence analysis of novel implicit Peer triplets of two-step nature with four stages for nonlinear ODE constrained optimal control problems. We combine the property of superconvergence of some standard Peer method for inner grid points with carefully designed starting and end methods to achieve order four for the state variables and order three for the adjoint variables in a first-discretize-then-optimize approach together with A-stability. The notion triplets emphasize that these three different Peer methods have to satisfy additional matching conditions. Four such Peer triplets of practical interest are constructed. In addition, as a benchmark method, the well-known backward differentiation formula BDF4, which is only A(73.3°)-stable, is extended to a special Peer triplet to supply an adjoint consistent method of higher order and BDF type with equidistant nodes. Within the class of Peer triplets, we found a diagonally implicit A(84°)-stable method with nodes symmetric in [0, 1] to a common center that performs equally well. Numerical tests with four well established optimal control problems confirm the theoretical findings also concerning A-stability.

Uncontrolled Keywords: implicit Peer two-step methods, BDF-methods, nonlinear optimal control, first-discretize-then-optimize, discrete adjoints
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-224527
Additional Information:

This article belongs to the Section Analysis of Algorithms and Complexity Theory

Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 10 Oct 2022 12:47
Last Modified: 14 Nov 2023 19:05
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/22452
PPN: 500268002
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