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SUMMARY:Nonlinear Observers with a Contracting Riemannian Distance - Ricar
 do G. Sanfelice\, University of California\, Santa Cruz
DTSTART:20150520T130000Z
DTEND:20150520T140000Z
UID:TALK59491@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:We study the convergence property of nonlinear observers for n
 onlinear systems using Riemannian metrics as a measure of the distance bet
 ween state and estimate. We show that the existence of an observer guarant
 eeing the property that a Riemannian distance between system and observer 
 solutions is nonincreasing (decreasing) is such that the Lie derivative of
  the Riemannian metric along the system vector field is nonpositive (negat
 ive) in the tangent space to the output function level sets. Also\, if the
  observer has an infinite gain margin then the level sets of the output fu
 nction have to be geodesically convex. Conversely\, if these two propertie
 s are satisfied\, then there exists an observer that has an infinite gain 
 margin with Riemannian metric that is decreasing along solutions. We show 
 that the existence of such a contracting metric is related to the observab
 ility of the system’s linearization along its solutions. Moreover\, the 
 problem of designing a Riemannian metric satisfying the said properties is
  also addressed for general systems as well as systems that are strongly d
 ifferentially observable (which leads to reduced-order observers). Example
 s illustrating the ideas and results are presented. The presented results 
 are part of joint work with Laurent Praly.\n\nShort bio:\nRicardo G. Sanfe
 lice is an Associate Professor in the Department of Computer Engineering a
 t the University of California\, Santa Cruz. He received his M.S. and Ph.D
 . degrees from UCSB in 2004 and 2007\, respectively. He held a Postdoctora
 l Associate position at MIT during 2007 and 2008\, and afterwards visited 
 the Centre Automatique et Systemes at the Ecole de Mines de Paris for four
  months. He is the recipient of the 2013 SIAM Control and Systems Theory P
 rize\, the NSF CAREER award\, the Air Force Young Investigator Research Aw
 ard\, the 2010 IEEE Control Systems Magazine Outstanding Paper Award\, and
  the 2012 STAR Higher Education Award for his contributions to STEM educat
 ion. His research interests are in modeling\, stability\, robust control\,
  observer design\, and simulation of nonlinear and hybrid systems with app
 lications to power systems\, biology\, and aerospace.
LOCATION:Cambridge University Engineering Department\, LR5
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