Control of Integrable Hamiltonian Systems and Degenerate Bifurcations
Pattern Formation and Solitons
2009-11-10 v2
Abstract
We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both dissipative and conservative controllers are considered. We show that the shear flow structure of the undriven system causes a Takens-Bogdanov birfurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrodinger equation.
Keywords
Cite
@article{arxiv.nlin/0306018,
title = {Control of Integrable Hamiltonian Systems and Degenerate Bifurcations},
author = {C. W. Kulp and E. R. Tracy},
journal= {arXiv preprint arXiv:nlin/0306018},
year = {2009}
}
Comments
25 pages, 11 figures, resubmitted to Physical Review E March 2004 (originally submitted June 2003), added content and references