Nonlinear and linear dynamical systems

Research project P 14438 Nonlinear and linear dynamical systems Manfred DEISTLER 08.05.2000 The aim of this project is, to develop and analyze methods and tools for system identification. The emphasis is laid upon nonlinear dynamical systems, in particular recurrent neural networks, but also other model classes. will be considered. The project will contain three main areas of research: 1. Subspace Algorithms: These algorithms are used for the identification of linear dynamical systems. Due to their numerical properties, subspace algorithms are an attractive alternative to the more classical maximum. likelihood methods. Their statistical properties in the stationary, feedback free case are well established by now. Here the still unsolved problem of asymptotic efficience shall be treated. Additionally, the emphasis of this part of the project will be on the evaluation of the statistical and numerical properties of the estimates obtained by using subspace methods for the unit root, case, observed mostly in economic data sets, and, also in the case of output feedback, known as the `closed loop` case in the engineering literature. 2. Parametrization of linear dynamic systems: This part of the project will deal with numerical and statistical properties of recently proposed local parametrizations and balanced canonical forms. The main idea of these parametrizations is to choose local coordinates in order to achieve superior numerical properties as compared to the case, where canonical forms are used for the identification. These pardmetrizations will also be compared with more traditional approaches. 3. Recurrent neural networks: Although neural networks are used widely in the systems engineering community, the statistical foundations especially of recurrent networks are not sufficiently developed. The significance of neural networks lies in the fact, that they can represent many real world phenomena and thus are an attractive model class for many applications both in industry and economy. The aim of this part of the project is to develop a structure theory and statistical properties of estimation algorithms analogous to the theory existing for the linear dynamical models.