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

Abstract

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.

Behaviour Prediction Framework in System Architecture Development

“…In his work [9], Diepold presented structured process modelling approach by extending the DSM to the DynS-DSM (Dynamical System DSM). The properties of structural analysis are thereby kept up during the whole modelling procedure, which results in a discrete-time representation of the system's dynamics.…”

“…Structural analysis and the effects of structural changes are thus directly transferable into the system's dynamics supporting a coupled system optimization. DynS-DSM approach is extended to a framework (called quad-I/HS), which supports modelling of hybrid dynamical systems [9].…”

“…In example given by Diepold et al [6], the mapping framework is implemented on very simple mechanical system (the ball-pen) in order to illustrate the potential of the proposed models for adjusting the structural design in consequence of the system's performance. In his work [9], Diepold presented structured process modelling approach by extending the DSM to the DynS-DSM (Dynamical System DSM). The properties of structural analysis are thereby kept up during the whole modelling procedure, which results in a discrete-time representation of the system's dynamics.…”

Research and Application of the Simulation Method for Product Development Process Based on System Dynamics

“…These models prioritize the stability and reliability of the product but do not give sufficient consideration to the factors that trigger dynamic changes in the process and the resulting dynamic change patterns. They are commonly used to depict the intricate structure of the product design process [13]; however, they only provide a static view of the design process and do not adequately capture or analyze dynamic complexity [14].…”