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SUMMARY:Minimum Seeking for Unstable Unmodeled Systems - Professor Mirosla
 v Krstic\, University of California\, San Diego
DTSTART:20131125T110000Z
DTEND:20131125T120000Z
UID:TALK48593@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:Extremum seeking (ES)\, a non-model-based optimization method 
 whose development begun in the 1920s\, has thus far remained limited to st
 able plants. Removing this limitation is a logical challenge because ES\, 
 at its core\, is a method for stabilization - of extrema of input-output m
 aps of systems in steady state. We introduce a framework in which ES solve
 s the problem of stabilization of general nonlinear systems affine in cont
 rol\, without requiring the knowledge of the system's input and drift vect
 or fields. In this framework a control Lyapunov function is being minimize
 d using ES\, whereas the plant's state assumes implicitly a role of a vect
 or-valued integrator in the learning portion of the ES algorithm. The math
 ematical machinery behind the new approach is a combination of the Lie bra
 cket averaging method of Gurvits\, Sussmann\, and coworkers (an alternativ
 e to the conventional integration-based Krylov-Bogolyubov averaging) and o
 f an approximation-based semiglobal practical stability theory of Moreau a
 nd Aeyels. When applied to linear systems\, the ES approach solves the cla
 ssical challenge in adaptive control\, posed by Morse\, of stabilization o
 f systems with unknown control directions. Unlike the approach with Nussba
 um gain functions\, which provides a classical solution to this problem\, 
 the ES approach achieves stability even when the control directions change
  rapidly with time. 
LOCATION:Cambridge University Engineering Department\, LR3B
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