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Tackling two drawbacks of polynomial nonlinear state-­ space models

vrijdag, 22 juni, 2012 - 17:00
Campus: Brussels Humanities, Sciences & Engineering campus
Anne Van Mulders

System identification aims at fitting a mathematical model to real-life observations of the
world. For example, you might measure the sound of music in two places: directly (in the
same room as the source) and from behind a wall. The sound behind the wall is then a
muffled version of the original sound, with the high tones often more damped than the low
tones. The relation between the two measurements can be described by a model and
characterizes the acoustic behavior of the wall. This model can be used to simulate the sound
behind the wall for other pieces of music or more general sounds. Models hence have the
capability to predict new, unobserved real-life phenomena, what makes them very useful in
engineering, but also in economics, in meteorology, etc.

Most of the phenomena or systems behave nonlinearly: a loudspeaker distorts the music, a
robot arm has internal friction, … Therefore, over the years, nonlinear models have gained
more interest and nowadays, a wide variety of nonlinear models is studied. One such model,
which has been successfully applied to several experimental setups, is the Polynomial
Nonlinear State-Space (PNLSS) model. It is highly flexible, but some of its drawbacks need
special attention. Dealing with those drawbacks is the subject of this thesis.

The first part presents an optimization method that is robust with respect to system and
model instabilities. The second part reduces the complexity of the model by retrieving the
underlying structure. With the methods in this thesis, it should be possible to deliver models
that are better suited for the user.