Extremum Seeking Control: Convergence Analysis

Prof. Dragan Nesic (University of Melbourne)

DATE: 2009-10-02
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU

ABSTRACT:
We summarize our recent work on non-local stability properties for a class of extremum seeking (ES) controllers that have attracted a great deal of research attention in the past decade. Their local stability properties were already investigated. We first show that semi-global practical convergence is possible if the controller parameters are carefully tuned and the objective function has a unique (global) extremum. An interesting tradeoff between the convergence rate and the size of the domain of attraction of the scheme is uncovered: the larger the domain of attraction, the slower the convergence of the algorithm. The amplitude, frequency and shape of the dither signal are important design parameters in the extremum seeking controller. In particular, we show that changing the amplitude of the dither adaptively can be used to deal with global extremum seeking in presence of local extrema. Moreover, we show that the convergence of the algorithm is proportional to the power of the dither signal. Consequently, the square-wave dither yields the fastest convergence among all dithers of the same frequency and amplitude. We consider extremum seeking of a class of bioprocesses to demonstrate our results and motivate some open research questions for multivalued objective functions.

BIO:
Dragan Nesic is currently is a Professor in the Department of Electrical and Electronic Engineering at The University of Melbourne. He was awarded a PhD from Systems Engineering, RSISE, Australian National University, Canberra in 1997 and he held several postdoctoral positions in Australia, Europe and US. He held an Australian Professorial Fellowship funded by the Australian Research Council and an Alexander von Humboldt Research Fellowship awarded by the Alexander von Humboldt Foundation in Germany. Prof. Nesic is a Fellow of the Institution of Electrical and Electronic Engineers (IEEE) and a Fellow of Institutions of Engineers Australia (IEAust). He is a Distinguished Lecturer of the Control Systems Society (CSS) of the IEEE. He is an associate editor for the following journals: Automatica, European Journal of Control and System & Control Letters. He also served as an associate editor for IEEE Transactions on Automatic Control. Prof. Nesic is the Chair of the CSS, IEEE Technical Committee for Nonlinear Systems and Control. His research interests are in the area of nonlinear systems and control, including networked and sampled-data control systems, extremum seeking control, singular perturbations, averaging and automotive control applications.

MEDIA:
ECC09-keynote_Dragan.pdf
video.html

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