Nonparametric identification of linear time-varying systems

Student thesis: Doctoral Thesis


Engineers and scientists want a reliable mathematical model of the observed phenomenon for understanding, design and control. System identification is a tool which allows the user to build models of dynamic systems from experimental noisy data. This is an interdisciplinary science which connects the world of control theory, data acquisition, signal processing, statistics, time series analysis and many other areas. In modeling and measurement techniques it is commonly assumed that the observed systems are linear time-invariant. This point of view is acceptable as long as the time variations of the systems are negligible. However, in some cases, this assumption is not satisfied and it leads to a very low accuracy of the estimates. In those cases, advanced modelling is needed taking into account the time-varying behavior of the model. In this thesis a very important class of systems, namely, the linear time varying systems are considered. The importance of these systems can be seen through some application examples. A good example from the electrical field is, for example a non-compensated transistor (in an operational amplifier) with a shifting offset-voltage: the higher the temperature, the higher the offset drift. The offset variations influence the system parameters and result in a time-varying behavior. The changing bio-impedance in the heart is also a good example from biomedical sciences. In chemistry, an interesting example can be the impedance changing due to the pitting corrosion in metals. It is already shown that LTV systems can be described by a two dimensional impulse response function. The challenge is that the time-varying two dimensional impulse response functions are not uniquely determined from a single set of input and output signals - like in the case of linear time invariant systems. Due to this non-uniqueness, the number of possible solutions is growing quadratically with the number of samples. To decrease the degrees of freedom, user-defined adjustable constraints will be imposed. This will be implemented by using two different approaches. First, a special two dimensional regularization technique is applied. The second implementation technique uses generalized two dimensional smoothing B-splines. Using the proposed methods high quality models can be built. This thesis involves the theoretical and implementational questions of the time-varying system identification.
Date of Award27 Oct 2015
Original languageEnglish
Awarding Institution
  • Vrije Universiteit Brussel
  • Budapest University of Technology and Economics
SupervisorJoannes Schoukens (Promotor), Istvan Kollar (Promotor), Istvan Vajk (Jury), Keith Richard Godfrey (Jury), J. Antoni (Jury), Steve Vanlanduit (Jury), Johan Deconinck (Jury) & John Lataire (Jury)


  • identification
  • linear time-varying systems

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