Lie bracket approximation of extremum seeking systems

Hans-Bernd Dürr; Miloš S. Stanković; Christian Ebenbauer; Karl Henrik Johansson

doi:10.1016/j.automatica.2013.02.016

journal article Jun 01, 2013

Lie bracket approximation of extremum seeking systems

Hans-Bernd Dürr Miloš S. Stanković Christian Ebenbauer Karl Henrik Johansson

Automatica Vol. 49 No. 6 pp. 1538-1552 · Elsevier BV

View at Publisher Save 10.1016/j.automatica.2013.02.016

Topics

No keywords indexed for this article. Browse by subject →

References

31

[1]

Bressan (2007)

[2]

Coddington (1955)

[3]

Dürr, H. B., Stanković, M. S., & Johansson, K. H. (2011a). Distributed positioning of autonomous mobile sensors with application to coverage control. In Proceedings of the 2011 American control conference, San Francisco (pp. 4822–4827). 10.1109/acc.2011.5991324

[4]

Dürr, H. B., Stanković, M. S., & Johansson, K. H. (2011b). A Lie bracket approximation for extremum seeking vehicles. In Proceedings of the 18th IFAC world congress, Milano (pp. 11393–11398). 10.3182/20110828-6-it-1002.02209

[5]

Frihauf "Nash equilibrium seeking in noncooperative games" IEEE Transactions on Automatic Control (2012) 10.1109/tac.2011.2173412

[6]

Gurvits, L. (1992). Averaging approach to nonholonomic motion planning. In Proceedings of the IEEE international conference on robotics and automation, vol. 2 (pp. 2541–2546). 10.1109/robot.1992.220059

[7]

Hale (1969)

[8]

Khalil (2002)

[9]

Krstić (2003)

[10]

Krstic "Stability of extremum seeking feedback for general nonlinear dynamic systems" Automatica (2000) 10.1016/s0005-1098(99)00183-1

[11]

Kurzweil "Limit processes in ordinary differential equations" Journal of Applied Mathematics and Physics (1987) 10.1007/bf00945409

[12]

LaSalle, J. P. (1962). Asymptotic stability criterion. In Proceedings of the 13th symposium in applied mathematics of the American mathematical society, hydrodynamic instability (pp. 299–307). 10.1090/psapm/013/0136842

[13]

Li "Smooth time-periodic solutions for non-holonomic motion planning" (1992)

[14]

Marden "Cooperative control and potential games" IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics (2009) 10.1109/tsmcb.2009.2017273

[15]

Moase, W. H., Manzie, C., Nesic, D., & Mareels, I. M. Y. (2010). Extremum seeking from 1922 to 2010. In 29th Chinese control conference (pp. 14–26).

[16]

Potential Games

Dov Monderer, Lloyd S. Shapley

Games and Economic Behavior 1996 10.1006/game.1996.0044

[17]

Moreau "Practical stability and stabilization" IEEE Transactions on Automatic Control (2000) 10.1109/9.871771

[18]

Moreau "Trajectory-based local approximations of ordinary differential equations" SIAM Journal on Control and Optimization (2003) 10.1137/s0363012900370776

[19]

Nash "Non-cooperative games" Annals of Mathematics (1951) 10.2307/1969529

[20]

Nathanson (1964)

[21]

Sanders (2007)

[22]

Stanković "Distributed seeking of Nash equilibria with applications to mobile sensor networks" IEEE Transactions on Automatic Control (2012) 10.1109/tac.2011.2174678

[23]

Stanković, M. S., & Stipanović, D. M. (2009). Discrete time extremum seeking by autonomous vehicles in a stochastic environment. In Proceedings of the 48th IEEE conference on decision and control, Shanghai (pp. 4541–4546). 10.1109/cdc.2009.5400504

[24]

Stanković "Extremum seeking under stochastic noise and applications to mobile sensors" Automatica (2010) 10.1016/j.automatica.2010.05.005

[25]

Sussmann, H. J., & Liu, W. (1991). Limits of highly oscillatory controls and approximation of general paths by admissible trajectories. In Proceedings of the 30th IEEE conference on decision and control (pp. 437–442). 10.1109/cdc.1991.261338

[26]

Sussmann "Lie bracket extensions and averaging: the single-bracket case" (1992)

[27]

Tan "On non-local stability properties of extremum seeking control" Automatica (2006) 10.1016/j.automatica.2006.01.014

[28]

Teel, A. R., Peuteman, J., & Aeyels, D. (1998). Global asymptotic stability for the averaged implies semi-global practical asymptotic stability for the actual. In Proceedings of the 37th IEEE conference on decision and control, vol. 2 (pp. 1458–1463). 10.1109/cdc.1998.758492

[29]

Wolpert, D. H. (2003). Theory of collective intelligence. Technical report, June 21. NASA Ames Research Center, Moffett Field, CA 95033.

[30]

Zhang "Source seeking with nonholonomic unicycle without position measurement and with tuning of forward velocity" Systems and Control Letters (2007) 10.1016/j.sysconle.2006.10.014

[31]

Zhang "Extremum seeking for moderately unstable systems and for autonomous vehicle target tracking without position measurements" Automatica (2007) 10.1016/j.automatica.2007.03.009

Cited By

203

100 years of extremum seeking: A survey

Alexander Scheinker · 2024

Automatica

Extremum-Seeking Regulator for a Class of Nonlinear Systems With Unknown Control Direction

Shimin Wang, Martin Guay · 2024

IEEE Transactions on Automatic Cont...

Practical prescribed-time seeking of a repulsive source by unicycle angular velocity tuning

Velimir Todorovski, Miroslav Krstic · 2023

Automatica

Recursive Averaging With Application to Bio-Inspired 3-D Source Seeking

Mahmoud Abdelgalil, Haithem Taha · 2022

IEEE Control Systems Letters

Finite-Time Stabilization of Linear Systems With Unknown Control Direction via Extremum Seeking

Adriano Mele, Gianmaria De Tommasi · 2022

IEEE Transactions on Automatic Cont...

Extremum Seeking Control for a Class of Nonholonomic Systems

Raik Suttner · 2020

SIAM Journal on Control and Optimiz...

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

Christophe Labar, Emanuele Garone · 2019

Automatica

On a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties

Victoria Grushkovskaya, Alexander Zuyev · 2018

Automatica

A framework for a class of hybrid extremum seeking controllers with dynamic inclusions

Jorge I. Poveda, Andrew R. Teel · 2017

Automatica

Distributed Nash Equilibrium Seeking by a Consensus Based Approach

Guoqiang Hu · 2017

IEEE Transactions on Automatic Cont...

Bounded extremum seeking with discontinuous dithers

Alexander Scheinker, David Scheinker · 2016

Automatica

Singularly Perturbed Lie Bracket Approximation

Hans-Bernd Dürr, Miroslav Krstic · 2015

IEEE Transactions on Automatic Cont...

Extremum seeking with bounded update rates

Alexander Scheinker, Miroslav Krstic · 2014

Systems & Control Letters

Non-C2 Lie Bracket Averaging for Nonsmooth Extremum Seekers

Alexander Scheinker, Miroslav Krstic · 2013

Journal of Dynamic Systems, Measure...

Metrics

203

Citations

31

References

Details

Published: Jun 01, 2013
Vol/Issue: 49(6)
Pages: 1538-1552

Authors

Karl Henrik Johansson

Cite This Article

Hans-Bernd Dürr, Miloš S. Stanković, Christian Ebenbauer, et al. (2013). Lie bracket approximation of extremum seeking systems. Automatica, 49(6), 1538-1552. https://doi.org/10.1016/j.automatica.2013.02.016

Lie bracket approximation of extremum seeking systems

You May Also Like