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Title: Extremum seeking with bounded update rates

Journal Article · · Systems & Control Letters
 [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

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.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-06NA25396
OSTI ID:
1193440
Report Number(s):
LA-UR-13-28230; PII: S0167691113002120
Journal Information:
Systems & Control Letters, Vol. 63, Issue C; ISSN 0167-6911
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 75 works
Citation information provided by
Web of Science

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Cited By (5)

Dynamic angular velocity turning for extremum seeking control of a two-dimensional mobile robot with external disturbances journal May 2019
On extremum seeking controllers based on the Lie bracket approximation in domains with obstacles journal December 2018
Constrained extremum seeking stabilization of systems not affine in control: Extremum Seeking Stabilization of Systems Not Affine in Control journal July 2017
Lie bracket approximation-based extremum seeking with vanishing input oscillations journal November 2021
On a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties text January 2017

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