Name
Title | ||
|---|---|---|
Nonlinear Adaptive Stabilization Of A Class Of Planar Slow-Fast Systems At A Non-Hyperbolic Point |
Abstract | ||
|---|---|---|
Non-hyperbolic points of slow-fast systems ( also known as singularly perturbed ordinary differential equations) are responsible for many interesting behavior such as relaxation oscillations, canards, mixed-mode oscillations, etc. Recently, the authors have proposed a control strategy to stabilize nonhyperbolic points of planar slow-fast systems. Such strategy is based on geometric desingularization, which is a well suited technique to analyze the dynamics of slow-fast systems near non-hyperbolic points. This technique transforms the singular perturbation problem to an equivalent regular perturbation problem. This papers treats the nonlinear adaptive stabilization problem of slow-fast systems. The novelty is that the point to be stabilized is non-hyperbolic. The controller is designed by combining geometric desingularization and Lyapunov based techniques. Through the action of the controller, we basically inject a normally hyperbolic behavior to the fast variable. Our results are exemplified on the van der Pol oscillator. |
Year | Venue | Field |
|---|---|---|
2017 | 2017 AMERICAN CONTROL CONFERENCE (ACC) | Lyapunov function,Control theory,Nonlinear system,Ordinary differential equation,Computer science,Control theory,Adaptive system,Van der Pol oscillator,Control engineering,Singular perturbation,Manifold |
DocType | ISSN | Citations |
Conference | 0743-1619 | 2 |
PageRank | References | Authors |
0.44 | 2 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. Jardón-Kojakhmetov | 1 | 8 | 2.11 |
| Jacquelien M. A. Scherpen | 2 | 491 | 95.93 |
| Dunstano del Puerto-Flores | 3 | 10 | 2.93 |