A Framework Including Artificial Neural Networks in Modelling Hybrid Dynamical Systems

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 sys-tems using hybrid state automata, and into modelling by and training of neural nets for dynam-ic 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 mathe-matical 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 re-placement of the entire hybrid system applying neural networks. The defined formalism stand-ardises the use of feed-forward networks in hybrid modelling and enables an analysis of differ-ent network structures.