Software toolbox for Linear and nonlinear system identification

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 this project, implemented in the software developed here, are: Parametrization: The property of parametrizations, for linear systems, in particular of the so called balanced realizations, is described. 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 were developed. In addition a test, whether this equivalence class contains a causal system, are constructed. The statistical properties of these algorithms are also evaluated. Regularization and complexity: A second approach, to overcome the numerical problems in identification of MIMO systems, relies on regularization methods. The statistical properties of such methods are exploited. These regularization methods seem to be promising also for the identification of nonlinear models (e.g. neural networks). The results for the linear case are generalized to certain classes of nonlinear systems.