Skip to main content
SpringerLink
Log in

Optimal Control for Discrete Fractional Systems

  • Conference paper
  • First Online:
Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

Abstract

In the paper optimal control problem for fractional discrete-time systems with quadratic performance index has been formulated and solved using the dynamic programming approach. New method for numerical computation of optimal control via the solution of dynamic programming problem has been presented. The efficiency of the method has been demonstrated on numerical example and illustrated by graphical representations. Graphs also show the differences between the fractional and integer-order systems theory.

This work was partially funded with Warsaw University of Technology grant.

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

Access this chapter

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
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)

    MATH  Google Scholar 

  2. Naidu, D.S.: Optimal Control Systems. Electrical Engineering. CRC Press Inc., Boca Raton (2002)

    Google Scholar 

  3. Podlubny, I.: Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. Academic Press (1999)

    Google Scholar 

  4. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science, New York (1993)

    Google Scholar 

  5. Agrawal, O.: A general finite element formulation for fractional variational problems. J. Math. Anal. Appl. 337(1), 1–12 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Frederico, G., Torres, D.: Fractional conservation laws in optimal control theory. Nonlinear Dyn. 53(3), 215–222 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jelic, Z., Petrovacki, N.: Optimality conditions and a solution scheme for fractional optimal control problems. Struct. Multidiscip. Optim. 38(6), 571–581 (2008)

    Article  MathSciNet  Google Scholar 

  8. Sierociuk, D., Vinagre, B.: Infinite horizon state-feedback LQR controller for fractional problems. In: Proceedings of \(49^{th}\) IEEE Conference on Decision and Control, pp. 6674–6679. Atlanta, USA (2010)

    Google Scholar 

  9. Sierociuk, D., Tejado, I., Vinagre, B.: Improved fractional Kalman filter and its application to estimation over lossy networks. Signal Process. 91(3), 542–552 (2011)

    Article  MATH  Google Scholar 

  10. Sierociuk, D., Dzielinski, A.: Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation. International. Int. J. Appl. Math. Comput. Sci. 16(1), 129–140 (2006)

    MathSciNet  MATH  Google Scholar 

  11. Dzielinski, A., Czyronis, P.: Dynamic programming for discrete-time fractional systems. In: Proceedings of The \(19^{th}\) IFAC World Congress, pp. 2003–2009. Cape Town, South Africa (2014)

    Google Scholar 

  12. Dzielinski, A., Czyronis, P.: Computer algorithms for solving optimization problems for discrete-time fractional systems. In: Proceedings of the European Control Conference, pp. 4009–4014. Zurich, Switzerland (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Control and Industrial Electronics, Warsaw University of Technology, Kloszykowa 75, 00-662, Warsaw, Poland

    Andrzej Dzieliński

Authors
  1. Andrzej Dzieliński
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrzej Dzieliński .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Dzieliński, A. (2017). Optimal Control for Discrete Fractional Systems. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45474-0_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation