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CATEGORIES:CUED Control Group Seminars
SUMMARY:Minimum Seeking for Unstable Unmodeled Systems - P
rofessor Miroslav Krstic\, University of Californi
a\, San Diego
DTSTART;TZID=Europe/London:20131125T110000
DTEND;TZID=Europe/London:20131125T120000
UID:TALK48593AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/48593
DESCRIPTION:Extremum seeking (ES)\, a non-model-based optimiza
tion method whose development begun in the 1920s\,
has thus far remained limited to stable plants. R
emoving this limitation is a logical challenge bec
ause ES\, at its core\, is a method for stabilizat
ion - of extrema of input-output maps of systems i
n steady state. We introduce a framework in which
ES solves the problem of stabilization of general
nonlinear systems affine in control\, without requ
iring the knowledge of the system's input and drif
t vector fields. In this framework a control Lyapu
nov function is being minimized using ES\, whereas
the plant's state assumes implicitly a role of a
vector-valued integrator in the learning portion o
f the ES algorithm. The mathematical machinery beh
ind the new approach is a combination of the Lie b
racket averaging method of Gurvits\, Sussmann\, an
d coworkers (an alternative to the conventional in
tegration-based Krylov-Bogolyubov averaging) and o
f an approximation-based semiglobal practical stab
ility theory of Moreau and Aeyels. When applied to
linear systems\, the ES approach solves the class
ical challenge in adaptive control\, posed by Mors
e\, of stabilization of systems with unknown contr
ol directions. Unlike the approach with Nussbaum g
ain functions\, which provides a classical solutio
n to this problem\, the ES approach achieves stabi
lity even when the control directions change rapid
ly with time.
LOCATION:Cambridge University Engineering Department\, LR3B
CONTACT:Tim Hughes
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