Extremum Seeking Control
In many situations, one aims at steering a dynamical system so as to optimize a given process variable, the cost, by acting on some other process variables, the system inputs. One may think, for instance, to the case of wind turbines. There, a typical goal is to maximize the produced power, by acting on the generator speed. Another example is the battery charging, where one aims to minimize the charging time, by selecting a suited current/voltage profile.
Extremum Seeking Control denotes a class of model-free adaptive (learning) algorithms able to achieve this objective, by only using the on-line measurement of the cost. They may thus be applied when the relation between the cost and the control inputs is unknown, or present significant uncertainties (e.g. in the case of wind turbines, the wind speed may not be accurately measured, preventing an accurate determination of the optimal rotational speed at each time instant).
Our research focuses on the development of methods to analyse and design extremum seeking systems by using Lie-bracket approximations. In particular, we design extremum seeking algorithms able to account for constraints, that may be implemented in a distributed way, or that include partial model information.
Related Publications
| Title | Authors and Contributors |
|---|---|
| Gradient Approximation and Multi-Variable Derivative-Free Optimization based on Non-Commutative Maps (2021) Preprint | Feiling, Jan Belabbas, Mohamed-Ali Ebenbauer, Christian Johannes |
| Gradient-Based Extremum Seeking: Performance Tuning via Lie Bracket Approximations In: 2018 European Control Conference (ECC) : 12-15 June 2018 / Marios M. Polycarpou, general chair, 2018 European Control Confernce (president, European Control Association (EUCA) ; [European Control Association (EUCA)] (2018), 2775-2780 Contribution to a book, Contribution to a conference proceedings [DOI: 10.23919/ECC.2018.8550562] | Labar, Christophe (Corresponding author) Feiling, Jan (Corresponding author) Ebenbauer, Christian Johannes (Corresponding author) |
| On a class of generating vector fields for the extremum seeking problem : Lie bracket approximation and stability properties In: Automatica : a journal of IFAC, the International Federation of Automatic Control, 94 (2018), 151-160 Journal Article [DOI: 10.1016/j.automatica.2018.04.024] | Grushkovskaya, Victoria (Corresponding author) Zuyev, Alexander Ebenbauer, Christian Johannes |
| Lie bracket approximation of extremum seeking systems In: Automatica, 49 (2013), 1538-1552 Journal Article [DOI: 10.1016/j.automatica.2013.02.016] | Dürr, Hans-Bernd (Corresponding author) Stankovic, Miloš S. Ebenbauer, Christian Johannes Johansson, Karl Henrik |