Sparse estimation or rational dynamical models
2012 (English)In: 16th IFAC Symposium on System Identification, IFAC , 2012, no PART 1, 983-988 p.Conference paper (Refereed)
In many practical situations, it is highly desirable to estimate an accurate mathematical model of a real system using as few parameters as possible. This can be motivated either from appealing to a parsimony principle (Occam's razor) or from the view point of the utilization complexity in terms of control synthesis, prediction, etc. At the same time, the need for an accurate description of the system behavior without knowing its complete dynamical structure often leads to model parameterizations describing a rich set of possible hypotheses; an unavoidable choice, which suggests sparsity of the desired parameter estimate. An elegant way to impose this expectation of sparsity is to estimate the parameters by penalizing the criterion with the ℓ 0 norm of the parameters, which is often implemented as solving an optimization program based on a convex relaxation (e.g. ℓ 1/ LASSO, nuclear norm, ⋯). However, in order to apply these methods, the (unpenalized) cost function must be convex. This imposes a severe constraint on the types of model structures or estimation methods on which these relaxations can be applied. In this paper, we extend the use of convex relaxation techniques for sparsity to general rational plant model structures estimated by using prediction error minimization. This is done by combining the LASSO and the Steiglitz-McBride approaches. To demonstrate the advantages of the proposed solution an extensive simulation study is provided.
Place, publisher, year, edition, pages
IFAC , 2012. no PART 1, 983-988 p.
, IFAC Proceedings Volumes (IFAC-PapersOnline), ISSN 1474-6670 ; 16
Control synthesis, Convex relaxation, Dynamical model, Dynamical structure, Estimation methods, Extensive simulations, Occam's razor, Optimization programs, Parameter estimate, Parameterizations, Parsimony principle, Prediction error minimizations, Real systems, Sparse estimation, Steiglitz-McBride approach, System behaviors, Control system synthesis, Mathematical models, Model structures, Parameter estimation, Relaxation processes, Estimation
IdentifiersURN: urn:nbn:se:kth:diva-105451DOI: 10.3182/20120711-3-BE-2027.00288ScopusID: 2-s2.0-84867071609ISBN: 978-390282306-9OAI: oai:DiVA.org:kth-105451DiVA: diva2:571293
Universite Libre de Bruxelles, 11 July 2012 through 13 July 2012, Bruxelles
FunderICT - The Next Generation
QC 201211222012-11-222012-11-212013-04-11Bibliographically approved