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Title: Extremum seeking with bounded update rates

Abstract

In this work, we present a form of extremum seeking (ES) in which the unknown function being minimized enters the system’s dynamics as the argument of a cosine or sine term, thereby guaranteeing known bounds on update rates and control efforts. We present general n-dimensional optimization and stabilization results as well as 2D vehicle control, with bounded velocity and control efforts. For application to autonomous vehicles, tracking a source in a GPS denied environment with unknown orientation, this ES approach allows for smooth heading angle actuation, with constant velocity, and in application to a unicycle-type vehicle results in control ability as if the vehicle is fully actuated. Our stability analysis is made possible by the classic results of Kurzweil, Jarnik, Sussmann, and Liu, regarding systems with highly oscillatory terms. In our stability analysis, we combine the averaging results with a semi-global practical stability result under small parametric perturbations developed by Moreau and Aeyels.

Authors:
 [1];  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). RF Control Group
  2. Univ. of California, San Diego, La Jolla, CA (United States). Dept. of Mechanical and Aerospace Engineering
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1193440
Report Number(s):
LA-UR-13-28230
Journal ID: ISSN 0167-6911; PII: S0167691113002120
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Systems & Control Letters
Additional Journal Information:
Journal Volume: 63; Journal Issue: C; Journal ID: ISSN 0167-6911
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; adaptive control; extremum seeking; autonomous agents; distributed optimization

Citation Formats

Scheinker, Alexander, and Krstić, Miroslav. Extremum seeking with bounded update rates. United States: N. p., 2013. Web. doi:10.1016/j.sysconle.2013.10.004.
Scheinker, Alexander, & Krstić, Miroslav. Extremum seeking with bounded update rates. United States. https://doi.org/10.1016/j.sysconle.2013.10.004
Scheinker, Alexander, and Krstić, Miroslav. Sat . "Extremum seeking with bounded update rates". United States. https://doi.org/10.1016/j.sysconle.2013.10.004. https://www.osti.gov/servlets/purl/1193440.
@article{osti_1193440,
title = {Extremum seeking with bounded update rates},
author = {Scheinker, Alexander and Krstić, Miroslav},
abstractNote = {In this work, we present a form of extremum seeking (ES) in which the unknown function being minimized enters the system’s dynamics as the argument of a cosine or sine term, thereby guaranteeing known bounds on update rates and control efforts. We present general n-dimensional optimization and stabilization results as well as 2D vehicle control, with bounded velocity and control efforts. For application to autonomous vehicles, tracking a source in a GPS denied environment with unknown orientation, this ES approach allows for smooth heading angle actuation, with constant velocity, and in application to a unicycle-type vehicle results in control ability as if the vehicle is fully actuated. Our stability analysis is made possible by the classic results of Kurzweil, Jarnik, Sussmann, and Liu, regarding systems with highly oscillatory terms. In our stability analysis, we combine the averaging results with a semi-global practical stability result under small parametric perturbations developed by Moreau and Aeyels.},
doi = {10.1016/j.sysconle.2013.10.004},
journal = {Systems & Control Letters},
number = C,
volume = 63,
place = {United States},
year = {Sat Nov 16 00:00:00 EST 2013},
month = {Sat Nov 16 00:00:00 EST 2013}
}

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Cited by: 75 works
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Works referenced in this record:

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Works referencing / citing this record:

Dynamic angular velocity turning for extremum seeking control of a two-dimensional mobile robot with external disturbances
journal, May 2019

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On extremum seeking controllers based on the Lie bracket approximation in domains with obstacles
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Constrained extremum seeking stabilization of systems not affine in control: Extremum Seeking Stabilization of Systems Not Affine in Control
journal, July 2017

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  • International Journal of Robust and Nonlinear Control, Vol. 28, Issue 2
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Lie bracket approximation-based extremum seeking with vanishing input oscillations
journal, November 2021