Jan Maciejowski's research: System identification and
Modelling
In order to design a control system, we need to model the behaviour of
the system being controlled. The models have to capture dynamic
behaviour (because most systems have some "memory" or "inertia"), so
they usually have the form of differential or difference equations.
"Black-box" modelling from data, without trying to model internal
physical mechanisms, is also called "system identification" (or "time
series analysis").
We often build linear models of systems. Even linear models give rise
to complex structural questions, such as:
Some of these questions are resolved by using balanced
parametrizations. A class of algorithms known as subspace
methods has proved to be very effective in practice. We have
explored the use of balanced parametrizations, and proposed improved
subspace methods. We have also developed extensions of subspace
methods for the identification of bilinear models (in which
state-input products are allowed).
A related question is how to approximate a given system model by a
simpler one. One way of formulating this problem leads to the optimal
approximation satisfying a set of polynomial equations, which are
known to have a finite set of solutions. We have investigated using
constructive algebra (Grobner basis) methods to find the complete set
of these solutions exactly, and hence to find the optimal approximate
model.
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This page last updated on 14 September 2005.