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Modeling and identification of nonlinear and impulsive systems
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2016 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

Mathematical modeling of dynamical systems plays a central roll in science and engineering. This thesis is concerned with the process of finding a mathematical model, and it is divided into two parts - one that concentrates on nonlinear system identification and another one where an impulsive model of testosterone regulation is constructed and analyzed.

In the first part of the thesis, a new latent variable framework for identification of a large class of nonlinear models is developed. In this framework, we begin by modeling the errors of a nominal predictor using a flexible stochastic model. The error statistics and the nominal predictor are then identified using the maximum likelihood principle. The resulting optimization problem is tackled using a majorization-minimization approach, resulting in a tuning parameter-free recursive identification method. The proposed method learns parsimonious predictive models. Many popular model structures can be expressed within the framework, and in the thesis it is applied to piecewise ARX models.

In the first part, we also derive a recursive prediction error method based on the Hammerstein model structure. The convergence properties of the method are analyzed by application of the associated differential equation method, and conditions ensuring convergence are given.

In the second part of the thesis, a previously proposed pulse-modulated feedback model of testosterone regulation is extended with infinite-dimensional dynamics, in order to better explain testosterone profiles observed in clinical data. It is then shown how the analysis of oscillating solutions for the finite-dimensional case can be extended to the infinte-dimensional case. A method for blind state estimation in impulsive systems is introduced, with the purpose estimating hormone concentrations that cannot be measured in a non-invasive way. The unknown parameters in the model are identified from clinical data and, finally, a method of incorporating exogenous signals portraying e.g. medical interventions is studied.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2016. , 210 p.
Series
Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-2516 ; 127
Keyword [en]
nonlinear system identification, modeling, impulsive systems, impulse detection
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-304837ISBN: 978-91-554-9721-7OAI: oai:DiVA.org:uu-304837DiVA: diva2:1034449
Public defence
2016-11-25, 2446, ITC, Lägerhyddsvägen 2, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2016-11-01 Created: 2016-10-11 Last updated: 2016-11-02

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Mattsson, Per
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Division of Systems and ControlAutomatic control
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