ISS-like properties in Lie-bracket approximations and application to extremum seeking

Automatica ◽  
2022 ◽  
Vol 136 ◽  
pp. 110041
Author(s):  
Christophe Labar ◽  
Christian Ebenbauer ◽  
Lorenzo Marconi
Keyword(s):  
Extremum Seeking ◽  
Lie Bracket

scholarly journals Lie bracket approximation of extremum seeking systems

Automatica ◽  
2013 ◽  
Vol 49 (6) ◽  
pp. 1538-1552 ◽  
Author(s):  
Hans-Bernd Dürr ◽  
Miloš S. Stanković ◽  
Christian Ebenbauer ◽  
Karl Henrik Johansson
Keyword(s):  
Extremum Seeking ◽  
Lie Bracket

Non-C2 Lie Bracket Averaging for Nonsmooth Extremum Seekers

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Alexander Scheinker ◽  
Miroslav Krstić
Keyword(s):  
Linear Time ◽  
Equilibrium Points ◽  
Stability Result ◽  
Extremum Seeking ◽  
Practical Stability ◽  
High Frequency Oscillation ◽  
Time Varying ◽  
Lie Bracket ◽  
Control Scheme ◽  
Persistency Of Excitation

A drawback of extremum seeking-based control is the introduction of a high frequency oscillation into a system's dynamics, which prevents even stable systems from settling at their equilibrium points. In this paper, we develop extremum seeking-based controllers whose control efforts, unlike that of traditional extremum seeking-based schemes, vanish as the system approaches equilibrium. Because the controllers that we develop are not differentiable at the origin, in proving a form of stability of our control scheme we start with a more general problem and extend the semiglobal practical stability result of Moreau and Aeyels to develop a relationship between systems and their averages even for systems which are nondifferentiable at a point. More specifically, in order to apply the practical stability results to our control scheme, we extend the Lie bracket averaging result of Kurzweil, Jarnik, Sussmann, Liu, Gurvits, and Li to non-C2 functions. We then improve on our previous results on model-independent semiglobal exponential practical stabilization for linear time-varying single-input systems under the assumption that the time-varying input vector, which is otherwise unknown, satisfies a persistency of excitation condition over a sufficiently short window.

Newton-based extremum seeking: A second-order Lie bracket approximation approach

Automatica ◽  
2019 ◽  
Vol 105 ◽  
pp. 356-367 ◽  
Author(s):  
Christophe Labar ◽  
Emanuele Garone ◽  
Michel Kinnaert ◽  
Christian Ebenbauer
Keyword(s):  
Second Order ◽  
Extremum Seeking ◽  
Approximation Approach ◽  
Lie Bracket

scholarly journals A Lie Bracket Approximation for Extremum Seeking Vehicles

2011 ◽  
Vol 44 (1) ◽  
pp. 11393-11398 ◽  
Author(s):  
Miloš S Stanković ◽  
Hans-Bernd Dürr ◽  
Karl Henrik Johansson
Keyword(s):  
Extremum Seeking ◽  
Lie Bracket

On extremum seeking controllers based on the Lie bracket approximation in domains with obstacles

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Victoria Grushkovskaya ◽  
Alexander Zuyev ◽  
Christian Ebenbauer
Keyword(s):  
Extremum Seeking ◽  
Lie Bracket

scholarly journals An Online Distributed Game Optimal Control for Heavy Haul Trains with Limited Communication

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Kai Gao ◽  
Zhiwu Huang ◽  
Jun Peng ◽  
Heng Li ◽  
Weirong Liu
Keyword(s):  
Optimal Control ◽  
Limited Range ◽  
Approximate Algorithm ◽  
Extremum Seeking ◽  
Global Information ◽  
Distributed Optimal Control ◽  
Lie Bracket ◽  
Heavy Haul ◽  
Heavy Haul Trains

For heavy haul trains, it is difficult to get global information due to the limited range of communication. This paper proposed a novel distributed optimal control based on game strategy, in which the global optimization is achieved by equilibrizing subsystems’ performance just utilizing local information. To online solve the game control, an efficient multivariable extremum seeking algorithm was adapted to approximate the partial differential equation deduced by optimal condition. The convergence of the proposed approximate algorithm is proved by constructing a fictitious Lie bracket system using Lyapunov function. Finally, the proposed distributed optimal control is valuated rigorously by case study according to the configuration of Daqin railway in China.

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