About this Book
Modelling dynamical systems by equations and modelling dynamical behaviour by neural nets are up to now different worlds. This PhD theses tries to combine both worlds in the area of hybrid dynamical systems. The author first introduces into modelling of hybrid dynamical systems using hybrid state automata, and into modelling by and training of neural nets for dynamic behaviour. Based on these two areas the author develops a framework, which allows to replace certain elements of hybrid models by neural networks, as sketched by the cover pictures. On a mathematical basis of extending hybrid state automata by neural nets and training methods, the thesis discusses three different possibilities for application: the approximation of local dynamic behaviour by neural nets, the prediction of the discrete processes by neural nets, and the replacement of the entire hybrid system applying neural networks. The defined formalism standardises the use of feed-forward networks in hybrid modelling and enables an analysis of different network structures.
About the Author
Stefanie Nadine Winkler studied Technical Mathematics at the Vienna University of Technology (TU Wien). Already in her bachelor curriculum she got involved in modelling and simulation. At master level, she put emphasis on two subjects – modelling methods and system simulation, and E-Learning for modelling and simulation and for basic mathematics. The first topic led her to a comparative master thesis on Comparative Mathematical Modelling of Groundwater Pollution, where she showed her interest and her abilities in analysing different modelling approaches. The work in E-Learning opened her a door into the TU Wien AKMATH Group, where she managed as research assistant the introductory mathematic courses for all beginners at TU Wien; here, she was mainly responsible for the E-Learning parts implemented via web in a symbolic language (MAPLE-TA). After the master thesis, she continued work in the E-Learning group, and she continued her scientific work in in PhD curriculum. She investigated various approaches for modelling hybrid systems, and she analysed neural network modelling, which she combined in her PhD on neural net modelling for hybrid systems. Her deep knowledge in the Maple-based Math E-Learning system resulted in consultancy work at European universities. After her PhD, she left university and started working for the management consulting firm d-fine Austria.