Performance Assessment of an Extremum Seeking Controller Using Continuation Methods

Duc H Nguyen*, Mark H Lowenberg , Simon A Neild

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

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Abstract

Assessing the performance of extremum seeking control – a class of model-free adaptive controller – remains a mathematically-intensive task that involves many restrictive assumptions due to the presence of a harmonic forcing signal. In this paper, we propose the use of bifurcation analysis and numerical continuation to provide a simple numerical framework for engineers to investigate the dynamics of an extremum seeking system. Using the example of a poorly-tuned auto-trim system on a nonlinear airliner model, the advantage of bifurcation analysis and continuation is demonstrated, including the ability to directly identify the oscillation amplitude and stability information. Other behaviours common in nonlinear harmonically-forced systems, such as existence of multiple solutions and bifurcations leading to multi-harmonic responses, are also detected. The purpose of this paper is to demonstrate the advantages of continuation in characterising the dynamics of an extremum seeking controller and to present this exciting controller scheme to the wider aeronautics audience.
Original languageEnglish
Title of host publicationProceedings of the 2022 CEAS EuroGNC conference
Place of PublicationBerlin, Germany
PublisherCouncil of European Aerospace Societies
Number of pages12
Publication statusPublished - 3 May 2022
EventCEAS EuroGNC 2022: Conference on Guidance, Navigation, and Control - Berlin Institute of Technology, Berlin, Germany
Duration: 3 May 20225 May 2022
https://eurognc2022.dglr.de/

Conference

ConferenceCEAS EuroGNC 2022
Country/TerritoryGermany
CityBerlin
Period3/05/225/05/22
Internet address

Keywords

  • extremum seeking
  • harmonic forcing
  • bifurcation analysis
  • dynamical systems

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