We consider differential equations dx/dt = f(x, l) where the parameter l = e t moves slowly through a bifurcation point of f. Such a dynamic bifurcation is often accompanied by a possibly dangerous jump transition. We construct smooth scalar feedback controls which avoid these jumps. For transcritical and pitchfork bifurcations, a small constant additive control is usually sufficient. For Hopf bifurcations, we have to construct a more elaborate control creating a suitable bifurcation with double zero eigenvalue.
Publié le : 1999-07-05
Classification:
Bifurcation theory,
nonlinear control theory,
singular perturbations,
dynamic bifurcations,
unfolding,
34E15, 58F14, 93D15,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-00130578,
author = {Berglund, Nils and Schneider, Klaus},
title = {Control of Dynamic Bifurcations},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00130578}
}
Berglund, Nils; Schneider, Klaus. Control of Dynamic Bifurcations. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00130578/