Assessing Performance of an Extremum Seeking Controller Using Continuation Methods

Abstract

In order to assess the performance of an extremum seeking controllers, many restrictive assumptions have to be made due to the presence of a harmonic forcing signal, and the process remains mathematically intensive. We propose the use of bifurcation analysis and numerical continuation to provide a simple numerical framework 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 promising controller scheme to the wider aeronautics audience.