Seminar Details
2014-01-28 (14.00) : Optimal experiment design for closed-loop identification: solution based on the central moment extension
At Euler building
Organized by Mathematical Engineering
Speaker :
Gevers, Michel
Abstract :
Optimal experiment design for system identification was a very active research topic in the 1970s : the results at that time focused on the minimization of different measures of the parameter covariance matrix. The research on this topic disappeared from the horizon for more than a decade. In the mid eighties new results became available that focused on quality criteria that took account of the objective for which the model was estimated. These results were based on Ljung's approximate variance formulae for the estimated transfer functions, under the assumption that the model order goes to infinity. Experiment design experienced a sudden revival of activity from around 2003 under a triple influence : the advent of new expressions for the variance of estimated quantities that did not require an assumption of model order going to infinity, the introduction of the concept of « least costly identification design » due to Xavier Bombois et al, and the development of new opti mal design techniques for identification that convert the optimization problem into a semi-definite program that can be solved using Linear Matrix Inequalities. In this talk we shall first review the development of optimal experiment design. We shall then present new results, developed with Roland Hildebrand, that allow one to solve the optimal closed loop experiment design problem, where the optimization is performed jointly with respect to the controller and the spectrum of the external excitation. Our latest results, to be presented at CDC 2013, allow a direct construction of the optimal pair «controller in the loop - external excitation spectrum». They are based on the so-called «central extension» in the classical Carathéodory moment extension problem, one of the most widely studied problems in the theory of stochastic processes; the central extension was initially introduced by Genin, Delsarte and Kamp in 1978.