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# Nonlinear dynamic systems: blind identification of block- oriented models, and instability under random inputs

Wednesday, 4 May, 2011 - 11:30
Campus: Brussels Humanities, Sciences & Engineering campus
K
auditorium P. Janssens
Laurent Vanbeylen
phd defence

Nonlinear dynamic systems are everywhere present in our daily life: a microchip, a loudspeaker, a
robot, a car, an airplane, a chemical plant, a bridge, ... These applications reveal both dynamic and
nonlinear behaviour. Dynamic means that the system's response is frequency dependent and that the
system has a memory, while nonlinear means that the response does not scale (linearly) with the input
amplitude. Till now, system identication has been mainly focussing on linear modelling. These linear
models, which try to give an accurate mathematical approximation of reality, can become inaccurate when
used for nonlinear dynamical systems. Hence, nonlinear models are needed. Besides providing insight
into the complex behaviour of dynamical systems, these (nonlinear) models can be used for simulation,
prediction, design, optimisation and control purposes.
The rst part of the thesis concentrates on the identication of certain types of nonlinear systems (e.g.
Wiener and Hammerstein systems). Usually, in system identication, the system's input and output are
both measured. But in some applications, one has no access to the input, e.g. the wind acting on a bridge
or building, or the unknown stock market input. In the cases where only output data are available, blind
identication becomes the only option. Blind identication is more involved than the classical identication
theory. In this work, the theoretical properties and also the impact of measurement noise disturbances are
analysed.
In a second part, the focus is put on the (in)stability of nonlinear dynamical systems. A system is
called stable if the response to a bounded input is bounded. In practice, the stability or instability of a
given physical system or model is often unknown. For linear systems the theory is well-established. In this
work, the aim is to construct tools for (automated) retrieval of stability information of nonlinear systems
(or models), assuming that the input is random.

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