Criteria for informative experiments with subspace identification

Abstract

Informative experiments are identification experiments which contain sufficient information for an identification algorithm to discriminate between different models in an intended model set. In this paper, a particular set of identification algorithms, namely subspace based identification, is considered. Criteria for experiments to be informative with these methods in the deterministic setup and the combined deterministic-stochastic setup are presented. It is pointed out that if these criteria are not satisfied, interesting phenomena, in which perfect cancellations of the deterministic components and the stochastic components occur in a subspace projection, may occur. It is further shown that such cancellations can indeed be avoided under mild conditions.

10. Acknowledgement

The authors are indebted to K. Glover and B. De Moor for valuable discussion and suggestions on this work. This work has been supported financially by the Natural Sciences and Engineering Research Council of Canada, the European Research Network in System Identification (European Commission Contracts ERB CHBG CT 920002, ERB FMRX CT98 0206), the Committee of Vice-Chancellors and Principals of the Universities of the United Kingdom, the Cambridge University Engineering Department, and Pembroke College, Cambridge.

Notes

That is, for any

, we have

if and only if

.

The term ‘consistently identifies’ refers to the fact that, when the ‘averaging’ operator

is used on real data, the identified system converges almost surely to the true system (up to a state-coordinate transformation) as T→∞