skip to main content
10.1145/2562059.2562135acmconferencesArticle/Chapter ViewAbstractPublication PagescpsweekConference Proceedingsconference-collections
research-article

A hyperdense semantic domain for hybrid dynamic systems to model different classes of discontinuities

Published: 15 April 2014 Publication History

Abstract

The physics of technical systems, such as embedded and cyber-physical systems, is frequently modeled using the notion of continuous time. The underlying continuous phenomena may, however, occur at a time scale much faster than the system behavior of interest. In such situations, it is desirable to approximate the detailed continuous-time behavior by discontinuous change. Two classes of discontinuous change can be identified: pinnacles and mythical modes. This work shows how pinnacles are well modeled using a hyperreal notion of time while a superdense notion of time applies well to mythical modes. Thus, the combination, called hyperdense time, is proposed to allow for the expression of the semantics of both pinnacles and mythical modes. Further, the hyperdense semantic domain is translated into a computational representation as a three-dimensional model of time. In particular, continuous-time behavior is mapped onto floating point numbers, while the mythical mode and pinnacle event iterations each map onto an integer dimension. A modified Newton's cradle is used as a case study and to illustrate the computational implementation.

References

[1]
R. Alur, C. Courcoubetis, T. A. Henzinger, and P.-H. Ho. Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In R. Grossman, A. Nerode, A. Ravn, and H. Rischel, editors, Lecture Notes in Computer Science, volume 736, pages 209--229. Springer-Verlag, 1993.
[2]
A. Benveniste, T. Bourke, B. Caillaud, and M. Pouzet. Non-standard semantics of hybrid systems modelers. Journal of Computer and System Sciences, 78(3):877--910, May 2012.
[3]
S. Bliudze and D. Krob. Modelling of complex systems: Systems as dataflow machines. Fundamenta Informaticae, 91:1--24, 2009.
[4]
T. Bourke and M. Pouzet. Zélus, a Synchronous Language with ODEs. In International Conference on Hybrid Systems: Computation and Control (HSCC 2013), Philadelphia, USA, April 8-11 2013. ACM.
[5]
P. Breedveld. Multibond graph elements in physical systems theory. Journal of the Franklin Institute, 319(1/2):1--36, January/February 1985.
[6]
P. C. Breedveld. Physical Systems Theory in Terms of Bond Graphs. PhD dissertation, University of Twente, Enschede, Netherlands, 1984.
[7]
P. C. Breedveld. The context-dependent trade-off between conceptual and computational complexity illustrated by the modeling and simulation of colliding objects. In CESA '96 IMACS Multiconference, Lille, France, July 1996. Ecole Centrale de Lille.
[8]
B. Brogliato. Nonsmooth Mechanics. Springer-Verlag, London, 1999. ISBN 1-85233-143-7.
[9]
H. Callen. Thermodynamics. John Wiley & Sons, Inc., New York/London, 1960.
[10]
K. Edström. Switched Bond Graphs: Simulation and Analysis. PhD dissertation, Linköping University, Sweden, 1999.
[11]
K. Edström, J.-E. Strömberg, U. Söderman, and J. Top. Modelling and simulation of a switched power converter. In F. E. Cellier and J. J. Granda, editors, 1997 International Conference on Bond Graph Modeling and Simulation (ICBGM '97), pages 195--200, Phoenix, AZ, Jan. 1997. Society for Computer Simulation.
[12]
H. Elmqvist, B. Bachmann, F. Boudaud, J. Broenink, D. Brück, T. Ernst, R. Franke, P. Fritzson, A. Jeandel, P. Grozman, K. Juslin, D. Kågedahl, M. Klose, N. Loubere, S. E. Mattsson, P. Mosterman, H. Nilsson, M. Otter, P. Sahlin, A. Schneider, H. Tummescheit, and H. Vangheluwe. Modelica™ - a unified object-oriented langauge for physical systems modeling: Language specification, Dec. 1999. version 1.3, http://www.modelica.org/.
[13]
G. Falk and W. Ruppel. Energie und Entropie: Eine Einführung in die Thermodynamik. Springer-Verlag, Berlin, Heidelberg, New York, 1976. ISBN 3-540-07814-2.
[14]
J. Friedman and J. Ghidella. Using model-based design for automotive systems engineering - requirements analysis of the power window example. In Proceedings of the SAE 2006 World Congress & Exhibition, pages CD-ROM: 2006-01-1217, Detroit, MI, Apr. 2006.
[15]
O. Heaviside. On the forces, stresses, and fluxes of energy in the electromagnetic field. Proceedings of the Royal Society of London, 50:126--129, 1891.
[16]
A. Hurd and P. Loeb. An Introduction to Nonstandard Real Analysis. Pure and Applied Mathematics. Elsevier Science, 1985.
[17]
Y. Iwasaki, A. Farquhar, V. Saraswat, D. Bobrow, and V. Gupta. Modeling time in hybrid systems: How fast is "instantaneous"? In 1995 International Conference on Qualitative Reasoning, pages 94--103, Amsterdam, May 1995. University of Amsterdam.
[18]
D. Karnopp, D. Margolis, and R. Rosenberg. Systems Dynamics: A Unified Approach. John Wiley and Sons, New York, 2 edition, 1990.
[19]
H. J. Keisler. Elementary Calculus: An Infinitesimal Approach. Prindle, Weber and Schmidt, Dover, 3 edition, 2012.
[20]
E. Lee and H. Zheng. Operational semantics of hybrid systems. In International Conference on Hybrid Systems: Computation and Control (HSCC 2005), pages 25--53, Zürich, Switzerland, Mar. 2005.
[21]
O. Maler, Z. Manna, and A. Pnueli. From timed to hybrid systems. In Real-Time: Theory in Practice, Lecture Notes in Computer Science, pages 447--484. Springer, 1992.
[22]
MathWorks®. MATLAB® and Simulink#174; product families, Sept. 2012.
[23]
P. J. Mosterman. Hybrid Dynamic Systems: A hybrid bond graph modeling paradigm and its application in diagnosis. PhD dissertation, Vanderbilt University, 1997.
[24]
P. J. Mosterman. HyBrSim - a modeling and simulation environment for hybrid bond graphs. Journal of Systems and Control Engineering, 216(1):35--46, 2002.
[25]
P. J. Mosterman and G. Biswas. Behavior generation using model switching a hybrid bond graph modeling technique. In F. E. Cellier and J. J. Granda, editors, 1995 International Conference on Bond Graph Modeling and Simulation (ICBGM '95), number 1 in Simulation, pages 177--182, Las Vegas, Jan. 1995. Society for Computer Simulation, Simulation Councils, Inc. Volume 27.
[26]
P. J. Mosterman and G. Biswas. Modeling discontinuous behavior with hybrid bond graphs. In 1995 International Workshop on Qualitative Reasoning, pages 139--147, Amsterdam, May 1995. University of Amsterdam.
[27]
P. J. Mosterman and G. Biswas. A theory of discontinuities in dynamic physical systems. Journal of the Franklin Institute, 335B(3):401--439, Jan. 1998.
[28]
P. J. Mosterman and G. Biswas. A java implementation of an environment for hybrid modeling and simulation of physical systems. In Proceedings of the International Conference on Bond Graph Modeling, pages 750--755, Mexico City, Mexico, Sept. 1999.
[29]
P. J. Mosterman, J. Ghidella, and J. Friedman. Model-based design for system integration. In Proceedings of The Second CDEN International Conference on Design Education, Innovation, and Practice, pages CD-ROM: TB-3-1 through TB-3-10, Kananaskis, Alberta, Canada, July 2005.
[30]
P. J. Mosterman, S. Prabhu, and T. Erkkinen. An industrial embedded control system design process. In Proceedings of The Inaugural CDEN Design Conference (CDEN'04), Montreal, Canada, July 2004. CD-ROM: 02B6.
[31]
P. J. Mosterman, G. Simko, and J. Zander. A hyperdense semantic domain for discontinuous behavior in physical system models. In Proceedings of the 7th International Workshop on Multi-Paradigm Modeling at the ACM/IEEE 16th International Conference on Model Driven Engineering Languages and Systems (MoDELS) conference, Miami, FL, Sept. 2013.
[32]
P. J. Mosterman and H. Vangheluwe. Computer automated multi-paradigm modeling in control system design. In Proceedings of the IEEE International Symposium on Computer-Aided Control System Design, pages 65--70, Anchorage, Alaska, Sept. 2000.
[33]
P. J. Mosterman, J. Zander, G. Hamon, and B. Denckla. A computational model of time for stiff hybrid systems applied to control synthesis. Control Engineering Practice, 20(1):2--13, 2012.
[34]
P. J. Mosterman, F. Zhao, and G. Biswas. An ontology for transitions in physical dynamic systems. In AAAI98, pages 219--224, July 1998.
[35]
T. Nishida and S. Doshita. Reasoning about discontinuous change. In Proceedings AAAI-87, pages 643--648, Seattle, Washington, 1987.
[36]
H. M. Paynter. Analysis and Design of Engineering Systems. The M.I.T. Press, Cambridge, Massachusetts, 1961.
[37]
A. Platzer. Differential dynamic logic for hybrid systems. Journal of Automated Reasoning, 41(2):143--189, 2008.
[38]
D. E. Post and L. G. Votta. Computational science demands a new paradigm. Physics Today, 58(8):35--41, Jan. 2005.
[39]
U. Söderman and J.-E. Strömberg. Switched bond graphs: Multiport switches, mathematical characterization and systematic composition of computational models. Technical Report LiTH-IDA-R-95-7, Department of Computer and Information Science, Linköping University, Linköping, Sweden, 1995.
[40]
Steering Committee for Foundations in Innovation for Cyber-Physical Systems. Foundations for Innovation: Strategic Opportunities for the 21st Century Cyber-Physical Systems - Connecting computer and information systems with the physical world. Technical report, National Institute of Standards and Technology (NIST), Mar. 2013.
[41]
J.-E. Strömberg, J. Top, and U. Söderman. Variable causality in bond graphs caused by discrete effects. In Proceedings of the International Conference on Bond Graph Modeling, pages 115--119, San Diego, California, 1993.

Cited By

View all
  • (2022)MOSFET Modelling for a Three-Level Inverter Circuit: A Hybrid Bond Graph ApproachIECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society10.1109/IECON49645.2022.9968725(1-5)Online publication date: 17-Oct-2022
  • (2020)Toward a Theory of Superdense Time in Simulation ModelsACM Transactions on Modeling and Computer Simulation10.1145/337948930:3(1-13)Online publication date: 31-May-2020
  • (2019)A new modeling interface for simulators implementing the discrete event system specificationProceedings of the Theory of Modeling and Simulation Symposium10.5555/3338246.3338253(1-12)Online publication date: 29-Apr-2019
  • Show More Cited By

Index Terms

  1. A hyperdense semantic domain for hybrid dynamic systems to model different classes of discontinuities

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    HSCC '14: Proceedings of the 17th international conference on Hybrid systems: computation and control
    April 2014
    328 pages
    ISBN:9781450327329
    DOI:10.1145/2562059
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

    Sponsors

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 15 April 2014

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. hybrid systems
    2. modeling
    3. physical systems
    4. physics
    5. semantics
    6. simulation

    Qualifiers

    • Research-article

    Conference

    HSCC'14
    Sponsor:

    Acceptance Rates

    HSCC '14 Paper Acceptance Rate 29 of 69 submissions, 42%;
    Overall Acceptance Rate 153 of 373 submissions, 41%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)2
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 26 Dec 2024

    Other Metrics

    Citations

    Cited By

    View all
    • (2022)MOSFET Modelling for a Three-Level Inverter Circuit: A Hybrid Bond Graph ApproachIECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society10.1109/IECON49645.2022.9968725(1-5)Online publication date: 17-Oct-2022
    • (2020)Toward a Theory of Superdense Time in Simulation ModelsACM Transactions on Modeling and Computer Simulation10.1145/337948930:3(1-13)Online publication date: 31-May-2020
    • (2019)A new modeling interface for simulators implementing the discrete event system specificationProceedings of the Theory of Modeling and Simulation Symposium10.5555/3338246.3338253(1-12)Online publication date: 29-Apr-2019
    • (2019)A New Modeling Interface for Simulators Implementing the Discrete Event System Specification2019 Spring Simulation Conference (SpringSim)10.23919/SpringSim.2019.8732882(1-12)Online publication date: Apr-2019
    • (2018)Handling overlapping collisionsProceedings of the Theory of Modeling and Simulation Symposium10.5555/3213187.3213190(1-12)Online publication date: 15-Apr-2018
    • (2018)Handling overlapping collisionsProceedings of the 4th ACM International Conference of Computing for Engineering and Sciences10.1145/3213187.3213190(1-12)Online publication date: 6-Jul-2018
    • (2016)On the representation of time in modeling & simulationProceedings of the 2016 Winter Simulation Conference10.5555/3042094.3042294(1571-1582)Online publication date: 11-Dec-2016
    • (2016)On the representation of time in modeling & simulation2016 Winter Simulation Conference (WSC)10.1109/WSC.2016.7822207(1571-1582)Online publication date: Dec-2016
    • (2015)Multi-domain model of steering system for an omnidirectional mobile robot2015 IEEE International Conference on Robotics and Biomimetics (ROBIO)10.1109/ROBIO.2015.7419081(2084-2090)Online publication date: Dec-2015

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media