Seminar Details
2012-02-28 (14.00) : Optimal experiment design for open and closed loop identification
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 1970's: the results at that time
focused on the minimization of different measures of the parameter
covariance matrix. The research on this topic disappeared 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 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", and the development of new optimal design
techniques for identification that convert the optimization problem
into semi-definite programs 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 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 results
are based on the partial positive definite matrix completion theorem.