Name
Title | ||
|---|---|---|
The multidimensional n-th order heavy ball method and its application to extremum seeking |
Abstract | ||
|---|---|---|
In this paper the extension of the heavy ball method to n-th order integrator dynamics is considered. We propose a gradient based controller that achieves to find the extremum of a function depending on multiple variables and prove asymptotic stability for all functions from the set of strongly convex functions. Furthermore, we propose a gradient-free extremum seeking controller that approximates the proposed gradient-based controller and prove practical asymptotic stability of the extremum using Lie bracket averaging techniques. The result does not rely on singular perturbation methods and provides a new approach to extremum seeking for dynamic maps. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/CDC.2014.7039796 | Decision and Control |
Keywords | Field | DocType |
asymptotic stability,convex programming,gradient methods,optimal control,perturbation techniques,Lie bracket averaging techniques,asymptotic stability,convex functions,dynamic maps,gradient-based controller,gradient-free extremum seeking controller,multidimensional nth order heavy ball method,nth order integrator dynamics,singular perturbation methods | Extremum estimator,Control theory,Mathematical optimization,Control theory,Integrator,Singular perturbation,Convex function,Exponential stability,Lie algebra,Mathematics | Conference |
ISSN | Citations | PageRank |
0743-1546 | 1 | 0.37 |
References | Authors | |
4 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simon Michalowsky | 1 | 6 | 3.21 |
| Christian Ebenbauer | 2 | 200 | 30.31 |