A Framework Including Artificial Neural Networks in Modelling Hyb Dynamical Systems

About the Book Modelling dynamical systems by equations and modelling dynamical behaviour by neural nets are up to now different worlds. This PhD thesis tries to combine these two worlds in the area of hybrid dynamical systems. The author first introduces modelling standards for hybrid dynamical systems using hybrid state automata followed by neural network practices 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, the prediction of the discrete processes 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 in general to enable an analysis of different network structures.