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SUMMARY:Adaptive design and control - Pronzato\, L (Universit de Nice Soph
 ia Antipolis)
DTSTART:20110720T080000Z
DTEND:20110720T090000Z
UID:TALK32105@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:There exist strong relations between experimental design and c
 ontrol\, for instance in situations where optimal inputs are constructed i
 n order to obtain precise parameter estimation in dynamical systems or whe
 n suitably designed perturbations are introduced in adaptive control to fo
 rce enough excitation into the system. The presentation will focus on adap
 tive design when the construction of an optimal experiment requires the kn
 owledge of the model parameters and current estimated values are substitut
 ed for unknown true values. This adaptation to estimated values creates de
 pendency among observations and makes the investigation of the asymptotic 
 behaviors of the design and estimator a much more complicated issue than w
 hen the design is specified independently of the observations. Also\, even
  if the system considered is static\, this adaptation introduces some feed
 back and the adaptive-design mechanism can be considered as a particular a
 daptive-control scheme. The role of experimental design in the asymptotic 
 properties of estimators will be emphasized. The assumption that the set o
 f experimental variables (design points) is finite facilitates the study o
 f the asymptotic properties of estimators (strong consistency and asymptot
 ic normality) in stochastic regression models. Two situations will be cons
 idered: adaptive D-optimal design and adaptive design with a cost constrai
 nt where the design should make a compromise between maximizing an informa
 tion criterion (D-optimality) and minimizing a cost (function optimization
 ). The case when the weight given to cost minimization asymptotically domi
 nates will be considered in detail in connection with self-tuning regulati
 on and self-tuning optimization problems.\n
LOCATION:Seminar Room 1\, Newton Institute
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