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Optimality analysis of the Two-Stage Algorithm for Hammerstein system identification
- Source :
- SYSID 2009-15th IFAC Symposium on System Identification, SYSID 2009-15th IFAC Symposium on System Identification, Jul 2009, Saint Malo, France. pp.320-325, ⟨10.3182/20090706-3-FR-2004.00052⟩
- Publication Year :
- 2009
- Publisher :
- Elsevier BV, 2009.
-
Abstract
- International audience; The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least-squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.
- Subjects :
- 0209 industrial biotechnology
Mathematical optimization
Generalization
System identification
Parameterized complexity
TEKNIKVETENSKAP
020206 networking & telecommunications
02 engineering and technology
General Medicine
Weighting
Nonlinear system identification
Nonlinear system
Matrix (mathematics)
Noise
020901 industrial engineering & automation
Colors of noise
[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
TECHNOLOGY
Mathematics
Subjects
Details
- ISSN :
- 14746670
- Volume :
- 42
- Database :
- OpenAIRE
- Journal :
- IFAC Proceedings Volumes
- Accession number :
- edsair.doi.dedup.....d3bf1306e15904de221e41b1af08bee8