Bifurcation preserving discretisations of optimal control problems

C. Offen, S. Ober-Blöbaum, in: n.d.

Download
OA 3.13 MB
Conference Paper | Accepted | English
Abstract
The first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisation methods are classically known for their excellent long term behaviour. As boundary value problems are posed on intervals of fixed, moderate length, it is not immediately clear whether methods can profit from structure preservation in this context. When parameters are present, solutions can undergo bifurcations, for instance, two solutions can merge and annihilate one another as parameters are varied. We will show that generic bifurcations of an OCP are preserved under discretisation when the OCP is either directly discretised to a discrete OCP (direct method) or translated into a Hamiltonian boundary value problem using first order necessary conditions of optimality which is then solved using a symplectic integrator (indirect method). Moreover, certain bifurcations break when a non-symplectic scheme is used. The general phenomenon is illustrated on the example of a cut locus of an ellipsoid.
Publishing Year
Conference
7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021
Conference Location
Berlin, Germany
Conference Date
2021-10-11 – 2021-10-13
LibreCat-ID

Cite this

Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal control problems.
Offen, C., & Ober-Blöbaum, S. (n.d.). Bifurcation preserving discretisations of optimal control problems. Presented at the 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021, Berlin, Germany.
@inproceedings{Offen_Ober-Blöbaum, title={Bifurcation preserving discretisations of optimal control problems}, author={Offen, Christian and Ober-Blöbaum, Sina} }
Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations of Optimal Control Problems,” n.d.
C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of optimal control problems,” presented at the 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021, Berlin, Germany.
Offen, Christian, and Sina Ober-Blöbaum. Bifurcation Preserving Discretisations of Optimal Control Problems.
All files available under the following license(s):
Creative Commons License:
CC-BYCreative Commons Attribution 4.0 International Public License (CC-BY 4.0)
Main File(s)
File Name
Access Level
OA Open Access
Last Uploaded
2021-07-29T09:37:49Z


Export

Marked Publications

Open Data LibreCat

Search this title in

Google Scholar