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 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.

[1]  Boris Lohmann,et al.  Discrete-modelling of process components interactions using the design structure matrix , 2010 .

[2]  Klaus Diepold,et al.  A Framework for DSM-Based Pre-Modelling Analysis of Complex Systems , 2009 .

[3]  Bernard P. Zeigler,et al.  Parallel discrete event simulation with application to continuous systems , 2003 .

[4]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[5]  Tyson R. Browning,et al.  Applying the design structure matrix to system decomposition and integration problems: a review and new directions , 2001, IEEE Trans. Engineering Management.

[6]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[7]  Martin Buss,et al.  Nonlinear Hybrid Dynamical Systems: Modeling, Optimal Control, and Applications , 2002 .

[8]  Christiaan J. J. Paredis,et al.  Modeling and Simulation Methods for Design of Engineering Systems , 2001, J. Comput. Inf. Sci. Eng..

[9]  D. V. Steward,et al.  The design structure system: A method for managing the design of complex systems , 1981, IEEE Transactions on Engineering Management.

[10]  Ali A. Yassine,et al.  A Multi-Domain Analysis Framework for Product Development , 2008 .

[11]  Onur M. Ülgen,et al.  An Algorithm for Converting Signed Digrapls to Forrester Schematics , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  B. Kendall.  Nonlinear Dynamics and Chaos , 2001 .

[13]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[14]  Udo Lindemann,et al.  Pre-selection of hybrid electric vehicle architectures during the initial design phase , 2007 .

[15]  Hong-Zhong Huang,et al.  Modeling the Product Development Process as a Dynamic System with Feedback , 2006, Concurr. Eng. Res. Appl..

[16]  Yoke San Wong,et al.  A dynamic model for managing overlapped iterative product development , 2008, Eur. J. Oper. Res..

[17]  Jason E Bartolomei.  Qualitative knowledge construction for engineering systems : extending the design structure matrix methodology in scope and procedure , 2007 .

[18]  Paul A. Fishwick,et al.  Handbook of Dynamic System Modeling , 2007 .

[19]  B. P. Ziegler,et al.  Theory of Modeling and Simulation , 1976 .

[20]  Andreas A. Linninger,et al.  A systems approach to mathematical modeling of industrial processes , 2000 .

[21]  Yaneer Bar-Yam,et al.  The Statistical Mechanics of Complex Product Development: Empirical and Analytical Results , 2007, Manag. Sci..

[22]  Udo Lindemann,et al.  Structural awareness in complex product design – the Multiple-Domain Matrix , 2007 .

[23]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[24]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..

[25]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

[26]  Michel Benaroch,et al.  Option-based management of technology investment risk , 2001, IEEE Trans. Engineering Management.

[27]  Karen Rudie,et al.  A survey of modeling and control of hybrid systems , 1997 .

[28]  J. Sterman.  Business Dynamics , 2000 .

[29]  Tyson R. Browning,et al.  Modeling and analyzing cost, schedule, and performance in complex system product development , 1998 .

[30]  菅野 道夫,et al.  Industrial applications of fuzzy control , 1985 .

[31]  J. Forrester.  Industrial Dynamics , 1997 .

[32]  Geoff Coyle,et al.  Qualitative and quantitative modelling in system dynamics: some research questions , 2000 .

[34]  Onur Ulgen,et al.  A sector approach to the: formulation of system dynamics models , 1978 .

[35]  Karsten Peters,et al.  Hybrid Systems Modeling Manufacturing and Front Dynamics , 2004 .

[36]  Ernesto Kofman,et al.  Discrete Event Simulation of Hybrid Systems , 2004, SIAM J. Sci. Comput..