Adaptive control for sequential design

• Autorzy: Roland Gautier , Luc Pronzato
• Języki publikacji: EN

Abstrakty

EN

The optimal experiment for estimating the parameters of a nonlinear regression model usually depends on the value of these parameters, hence the problem of designing experiments that are robust with respect to parameter uncertainty. Sequential designpermits to adapt the experiment to the value of the parameters, and can thus be considered as a robust design procedure. By designing theexperiments sequentially, one introduces a feedback of information, and thus dynamics, into the design procedure. Several sequential schemes, corresponding to different control policies, are considered. The optimal one corresponds to closed-loop control, and is solution of a stochastic dynamic-programming problem, which is extremely difficult to solve. A suboptimal strategy is proposed, which relies ona normal approximation of the future posterior of θ, independent of future observations. The design criterion obtained involves several mathematical expectations, which are approximated by Laplace method. Finally, stochastic approximation algorithms are also suggested to determine (sub)optimal sequential experiments without having to compute expectations.

Słowa kluczowe

EN

active control; adaptive control; certainty equivalence; closed-loop control; dynamic programming; open-loop feedback; optimal design; sequential design

Kategorie tematyczne

• 49L20: Dynamic programming method
• 62K05: Optimal designs
• 62L05: Sequential design
• 49N35: Optimal feedback synthesis

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2000
• Tom: 20
• Numer: 1
• Strony: 97-114

Daty

wydano

2000

otrzymano

1998-12-10

poprawiono

1999-04-24

Twórcy

autor

Roland Gautier

• CNRS/Université de Nice Sophia Antipolis, France

autor

Luc Pronzato

• CNRS/Université de Nice Sophia Antipolis, France

Bibliografia

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Identyfikatory

DOI

10.7151/dmps.1006