ConjugateLocus

This is accompanying source code for the publication

Bifurcation preserving discretisations of optimal control problems
Christian Offen, Sina Ober-Blöbaum
IFAC-PapersOnLine, Volume 54, Issue 19, 2021, Pages 334-339
DOI 10.1016/j.ifacol.2021.11.099

ArXiv, ArXiv author page, DOI

This GitHub Repository provides source code used fo numerical experiments in relation to the author's participation at the 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control 2021 (https://lhmnlc21.org/)

Computation of cusps and hyperbolic umbilics

Run ./variational/Locus3D_Cusps.ipynb to compute the two closed lines of cusps in the bifurcation diagram as well as the location of the four umbilic singularities.

Computation of full bifurcation diagram

Run ./variational/ComputeDataIsoSurf_FullLocus.ipynb and then ./variational/Isosurface.m to compute preimages of the sheets of folds of the bifurcation diagram. Run ./variational/MapIsoDataLocus.py to compute data of the conjugate locus and ./variational/LocusIsosurface.m to compute plots of these.

Computation of bifurcation diagram near a hyperbolic umbilic singularity

Run ./variational/UmbilicIsosurface_ComputeData.ipynb and then ./variational/UmbilicIsosurface_CriticalSet.m to compute preimages of the sheet of folds. Then continue with the last lines in ./variational/UmbilicIsosurface_ComputeData.ipynb. Finally, plot the locus with ./variational/UmbilicIsosurface_PlotLocus.m

All plots and figures are written to the folder ./variational/Plots. Computed data is written to ./variational/Data.

Alternative methods

For experiments with a non-variational method, use the corresponding scripts in subfolders of ./RK/ rather than ./variational/