Systematical hybrid state modelling of complex dynamical systems: The quad-I/HS framework

A three-phase modelling framework for systematically designing a general class of complex hybrid dynamical systems is proposed. The framework benefits from a recent decomposition principle, called DSM (dependency structure matrix), and results in a new hybrid state model paradigm supporting mathematical analyses. The two leading methods of complexity handling, modular modelling and closing under coupling, are therein combined. Each interaction is modelled as detailed as necessary by aligning the interaction knowledge to determined weighting coefficients. Proportional, functional and qualitative (linguistical) knowledge, which is included through Fuzzy-Logic, is considered. As not much is known about hybrid systems from the viewpoint of nonlinear dynamics, the framework's potential is shown by modelling an illustration example, considering attracting regions and a combination of bifurcations and chaos in different dynamical domains for stability analysis.