Informative data: how to get just sufficiently rich?

Prediction error identification requires that data be informative with respect to the chosen model structure. Whereas sufficient conditions for informative experiments have been available for a long time, there were surprisingly no results of necessary and sufficient nature. With the recent surge of interest in optimal experiment design, it is of interest to know the minimal richness required of the externally applied signal to make the experiment informative. We provide necessary and sufficient conditions on the degree of richness of the applied signal to generate an informative experiment, both in open loop and in closed loop. In a closed-loop setup, where identification can be achieved with no external excitation if the controller is of sufficient degree, our results provide a precisely quantifiable trade-off between controller degree and required degree of external excitation.


Published in:
Proceedings of 47th Conference on Decision and Control
Presented at:
47th Conference on Decision and Control, Cancun, Mexico, December 9-11, 2008
Year:
2008
Publisher:
IEEE CSS
Keywords:
Laboratories:




 Record created 2009-01-13, last modified 2018-03-17

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