Using feedback control and Newton iterations to track dynamically unstable phenomena in experiments
| dc.creator | Sieber, Jan | |
| dc.creator | Krauskopf, Bernd | |
| dc.date | 2009-03-18 | |
| dc.date.accessioned | 2026-07-07T12:53:36Z | |
| dc.date.available | 2026-07-07T12:53:36Z | |
| dc.description | If 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.description | 6 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0903.3144 | |
| dc.identifier | http://arxiv.org/abs/0903.3144 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223677 | |
| dc.subject | Dynamical Systems | |
| dc.title | Using feedback control and Newton iterations to track dynamically unstable phenomena in experiments | |
| dc.type | text |