Identification and the Information Matrix: How to Get Just Sufficiently Rich?

In prediction error identification, the information matrix plays a central role. Specifically, when the system is in the model set, the covariance matrix of the parameter estimates converges asymptotically, up to a scaling factor, to the inverse of the information matrix. The existence of a finite c...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on automatic control 2009-12, Vol.54 (12), p.2828-2840
Main Authors: Gevers, M., Bazanella, A.S., Bombois, X., Miskovic, L.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic properties
Automatic
Computer science
control theory
systems
Control systems
Control theory. Systems
Convergence
Covariance matrix
Educational programs
Engineering Sciences
Estimates
Exact sciences and technology
Experiment design
Identifiability
Information analysis
information matrix
input richness
Inverse
Mathematical models
Modelling and identification
Open loop systems
Parameter estimation
Robust control
Solid modeling
Systems engineering and theory
Tradeoffs
transfer of excitation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In prediction error identification, the information matrix plays a central role. Specifically, when the system is in the model set, the covariance matrix of the parameter estimates converges asymptotically, up to a scaling factor, to the inverse of the information matrix. The existence of a finite covariance matrix thus depends on the positive definiteness of the information matrix, and the rate of convergence of the parameter estimate depends on its ¿size¿. The information matrix is also the key tool in the solution of optimal experiment design procedures, which have become a focus of recent attention. Introducing a geometric framework, we provide a complete analysis, for arbitrary model structures, of the minimum degree of richness required to guarantee the nonsingularity of the information matrix. We then particularize these results to all commonly used model structures, both in open loop and in closed loop. In a closed-loop setup, our results provide an unexpected and precisely quantifiable trade-off between controller degree and required degree of external excitation.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2034199