Skip to main content
SpringerLink
Log in
Book cover

Advanced, Contemporary Control pp 1176–1188Cite as

Discrete-Time Switched Models of Non-linear Fractional-Order Systems

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1196))

Abstract

In the paper methods for modeling complex, non-linear dynamical systems of non-integer order, using the so-called switched models that are based on the dynamic change of local linear models, depending on the value of an appropriately chosen switching function are discussed. Such a multimodel approach enables a relatively simple description of properties of many complex processes encountered in technology, especially in electrical engineering, automation and robotics, but also in nature, biology, medicine and, for example, in economics. Although the theory of switched systems has been developing intensively since over a dozen or so years, many issues and problems have not been solved yet. This is particularly true for systems of non-integer order. In the paper three type of discrete-time dynamical switched models of fractional systems: Fuzzy Takagi-Sugeno Model (FO FTS), Piecewise Linear Model (FO PWL) and a new one – Mixed Logical Dynamical Model (FO MLD) are proposed. Some examples of applications of such models in control are given.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Mäkilä, P.M., Partington, J.R.: On linear models for nonlinear systems. Automatica 39, 1–13 (2003)

    Article  MathSciNet  Google Scholar 

  2. Fang, L., Lin, H., Antsaklis, P.J.: Stabilization and performance analysis for a class of switched systems. In: Proceedings of the 43rd IEEE Conference on Decision Control, Atlantis, pp. 1179–1180 (2004)

    Google Scholar 

  3. Lin, H., Antsaklis, P.J.: Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans. Autom. Control 54(2), 308–322 (2009)

    Article  MathSciNet  Google Scholar 

  4. Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Heidelberg (2011)

    Book  Google Scholar 

  5. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  6. Chen, Y.Q., Petráš, I., Xue, D.: Fractional order control. In: American Control Conference, St. Louis, pp. 1397–1410 (2009)

    Google Scholar 

  7. Domek, S.: Switched state model predictive control of fractional-order nonlinear discrete-time systems. In: Pisano, A., Caponetto, R. (eds.) Advances in Fractional Order Control and Estimation, Asian J. Control, Special Issue 15(3), 658–668 (2013)

    Google Scholar 

  8. Domek, S.: Piecewise affine representation of discrete in time, non-integer order systems. In: Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds.) Advances in the Theory and Applications of Non-integer Order Systems. LN in Electrical Engineering, vol. 257, pp. 149–160. Springer, Heidelberg (2013)

    Google Scholar 

  9. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D., Feliu, V.: Fractional Order Systems and Controls. Springer-Verlag, London (2010)

    Book  Google Scholar 

  10. Domek, S.: Fractional-order calculus in model predictive control. West Pomeranian University of Technology Academic Press, Szczecin (2013). (in Polish)

    Google Scholar 

  11. Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35, 407–427 (1999)

    Article  MathSciNet  Google Scholar 

  12. Domek, S.: Switched models of non-integer order. PWN, Warszawa (2019). (in Polish)

    Google Scholar 

  13. Ying, H.: Fuzzy Control and Modeling: Analytical Foundations and Applications. Wiley-IEEE Press, Piscataway (2000)

    Google Scholar 

  14. Sun, Z., Ge, S.S.: Switched Linear Systems: Control and Design. Springer, London (2005)

    Book  Google Scholar 

  15. Raman, R., Grossmann, I.E.: Relation between MILP modeling and logical inference for chemical process synthesis. Comput. Chem. Eng. 15(2), 73–84 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Control Engineering and Robotics, West Pomeranian University of Technology Szczecin, ul. Sikorskiego 37, 70-313, Szczecin, Poland

    Stefan Domek

Authors
  1. Stefan Domek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Domek .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Andrzej Bartoszewicz

  2. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Jacek Kabziński

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Domek, S. (2020). Discrete-Time Switched Models of Non-linear Fractional-Order Systems. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_98

Download citation

Publish with us

Policies and ethics

Search

Navigation