Using feedback control and Newton iterations to track dynamically unstable phenomena in experiments

dc.creatorSieber, Jan
dc.creatorKrauskopf, Bernd
dc.date2009-03-18
dc.date.accessioned2026-07-07T12:53:36Z
dc.date.available2026-07-07T12:53:36Z
dc.descriptionIf one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is a combination of classical feedback control and Newton iterations. Mechanical experiments on a parametrically excited pendulum have recently shown the practical feasibility of a simplified version of this algorithm: a combination of time-delayed feedback control (as proposed by Pyragas) and a Newton iteration on a low-dimensional system of equations. We show that both parts of the algorithm are uniformly stable near the saddle-node bifurcation: the experiment with time-delayed feedback control has uniformly stable periodic orbits, and the two-dimensional nonlinear system which has to be solved to make the control non-invasive has a well-conditioned Jacobian.
dc.description6 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0903.3144
dc.identifierhttp://arxiv.org/abs/0903.3144
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223677
dc.subjectDynamical Systems
dc.titleUsing feedback control and Newton iterations to track dynamically unstable phenomena in experiments
dc.typetext

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