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 mathemat...

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Bibliographic Details
Published inMathematical and computer modelling of dynamical systems Vol. 16; no. 4; pp. 347 - 371
Main Authors Diepold, Klaus J., Winkler, Franz J., Lohmann, Boris
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 19.11.2010
Taylor & Francis Ltd
Subjects
Chaos theory
complex systems
DSM/MDM
Dynamical systems
hybrid systems
non-linear dynamics
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Summary: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 non-linear 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.
ISSN:1387-3954
1744-5051
DOI:10.1080/13873954.2010.505059