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CEAS EuroGNC 2022

Performance Assessment of an Extremum Seeking Controller Using Continuation Methods
Duc H. Nguyen Research & Teaching Associate, University of Bristol, Department of Aerospace Engineering, BS8 1TR, Bristol, United Kingdom.
Mark H. Lowenberg Professor of Flight Dynamics, University of Bristol, Department of Aerospace Engineering, BS8 1TR, Bristol, United Kingdom.
Simon A. Neild Professor of Nonlinear Structural Dynamics, University of Bristol, Department of Aerospace Engineering, BS8 1TR, Bristol, United Kingdom.
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.
Keywords: extremum seeking; harmonic forcing; bifurcation analysis; dynamical systems
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Duc H. Nguyen, Mark H. Lowenberg, Simon A. Neild: Performance Assessment of an Extremum Seeking Controller Using Continuation Methods. Proceedings of the 2022 CEAS EuroGNC conference. Berlin, Germany. May 2022. CEAS-GNC-2022-001.
BibTeX entry:

@Incollection{CEAS-GNC-2022-001,
    authors = {Nguyen, Duc H. and Lowenberg, Mark H. and Neild, Simon A.},
    title = {Performance Assessment of an Extremum Seeking Controller Using Continuation Methods},
    booktitle = {Proceedings of the 2022 {CEAS EuroGNC} conference},
    address = {Berlin, Germany},
    month = may,
    year = {2022},
    note = {CEAS-GNC-2022-001}
}