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Analysis of the issue of consistency in identification for robust S. Gugercin, A.C. Antoulas, and H.P. Zhang
 

Summary: Analysis of the issue of consistency in identification for robust
control
S. Gugercin, A.C. Antoulas, and H.P. Zhang
Department of Electrical and Computer Engineering
Rice University
Houston, Texas 77251­1892, USA
e­mail: fserkan,aca,hpzhangg@rice.edu
fax: +1­713­348­5686
August 24, 2001
Abstract
Given measured data generated by a discrete­time linear system we propose a model consisting of a linear,
time­invariant system affected by norm­bounded perturbation. Under mild assumptions, the plants belonging
to the resulting uncertain family form a convex set. The approach depends on two key parameters: an a priori
given bound of the perturbation, and the input used to generate the data. It turns out that the size of the uncertain
family can be reduced by intersecting the model families obtained by making use of different inputs. Two
model validation problems in this identification scheme are analyzed, namely the worst and the best invalidation
problems. It turns out that while the former is a max­min optimization problem subject to a spherical constraint,
the latter is a quadratic optimization problem with a quadratic and a convex constraint.
For a given energy level, the worst invalidation problem computes the family of models which can be
invalidated for all possible noise sequences; i.e. the union of all possible uncertain families is obtained. The

  

Source: Antoulas, Athanasios C. - Department of Electrical and Computer Engineering, Rice University

 

Collections: Engineering