The project is concerned with problems in identification of linear and
nonlinear systems. Special emphasis is given to the case of multi-input
single-output (MISO)
and multi-input multi-output (MIMO) systems. The latter case shows
even in the linear case considerable more complexity when compared to the
single-input single-output (SISO) case. It should be noted that identification
of linear systems is a highly nonlinear task; the results obtained for
the linear case also have a pivotal character for identification of nonlinear
systems. The problems considered range from structure theory (realization
and parametrization) to estimation algorithms (including their evaluation).
The main topics of research will be:
Parametrization: The property of parametrizations, for linear systems,
in particular of the so called balanced realizations, will be investigated.
Subspace-methods: For 'large' MIMO systems the standard identification
procedures, like Maximum likelihood methods and Prediction error methods,
have high numerical complexity. The so called subspace methods (SSM) are
numerically faster, however their statistical properties have not been
fully investigated yet.
Algorithms for dynamic errors-in-variables models: here algorithms
for the estimation of the set of all observationally equivalent systems
shall be developed. In addition a test, whether this equivalence class
contains a causal system, shall be constructed. The statistical properties
of these algorithms will be evaluated.
Regularization and complexity: A second approach, to overcome the
numerical problems in identification of MIMO systems, might be the use
regularization methods. The statistical properties of such methods will
be evaluated. These regularization methods seem to be promising also for
the identification of nonlinear models (e.g. neural networks). The results
for the linear case will be generalized to certain classes of nonlinear
systems.
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