IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v159y2013i2d10.1007_s10957-013-0306-8.html
   My bibliography  Save this article

Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms

Author

Listed:
  • Xiang Wu

    (Southeast University)

  • Kanjian Zhang

    (Southeast University)

  • Changyin Sun

    (Southeast University)

Abstract

Under the framework of switched systems, this paper considers a multi-proportional-integral-derivative controller parameter tuning problem with terminal equality constraints and continuous-time inequality constraints. The switching time and controller parameters are decision variables to be chosen optimally. Firstly, we transform the optimal control problem into an equivalent problem with fixed switching instants by introducing an auxiliary function and a time-scaling transformation. Because of the complexity of constraints, it is difficult to solve the problem by conventional optimization techniques. To overcome this difficulty, a novel exact penalty function is introduced for these constraints. Furthermore, the penalty function is appended to the cost functional to form an augmented cost functional, giving rise to an approximate nonlinear parameter optimization problem that can be solved using any gradient-based method. Convergence results indicate that any local optimal solution of the approximate problem is also a local optimal solution of the original problem as long as the penalty parameter is sufficiently large. Finally, an example is provided to illustrate the effectiveness of the developed algorithm.

Suggested Citation

  • Xiang Wu & Kanjian Zhang & Changyin Sun, 2013. "Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 454-472, November.
  • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0306-8
    DOI: 10.1007/s10957-013-0306-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0306-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-013-0306-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. C.Y. Kaya & J.L. Noakes, 2003. "Computational Method for Time-Optimal Switching Control," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 69-92, April.
    2. H. Axelsson & Y. Wardi & M. Egerstedt & E. I. Verriest, 2008. "Gradient Descent Approach to Optimal Mode Scheduling in Hybrid Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 167-186, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matheus Henrique Marcolino & Roberto Kawakami Harrop Galvão & Karl Heinz Kienitz & Márcio Santos Vieira, 2017. "Determination of Periodic Trajectories of Dynamic Systems Subject to Switching Input Constraints," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 848-864, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. C. Y. Kaya & J. M. Martínez, 2007. "Euler Discretization and Inexact Restoration for Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 191-206, August.
    2. Elisha R. Pager & Anil V. Rao, 2022. "Method for solving bang-bang and singular optimal control problems using adaptive Radau collocation," Computational Optimization and Applications, Springer, vol. 81(3), pages 857-887, April.
    3. Michael McAsey & Libin Mou & Weimin Han, 2012. "Convergence of the forward-backward sweep method in optimal control," Computational Optimization and Applications, Springer, vol. 53(1), pages 207-226, September.
    4. Pierre Bonami & Alberto Olivares & Ernesto Staffetti, 2014. "Energy-Optimal Multi-Goal Motion Planning for Planar Robot Manipulators," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 80-104, October.
    5. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.
    6. Kaya, C. Yalcin, 2004. "Time-optimal switching control for the US cocaine epidemic," Socio-Economic Planning Sciences, Elsevier, vol. 38(1), pages 57-72, March.
    7. Yi Jiang & Yi He & Jie Sun, 2011. "Subdifferential properties of the minimal time function of linear control systems," Journal of Global Optimization, Springer, vol. 51(3), pages 395-412, November.
    8. Wenhui Luo & Xuewen Tan & Xiufen Zou & Qing Tan, 2023. "Optimal Treatment of Prostate Cancer Based on State Constraint," Mathematics, MDPI, vol. 11(19), pages 1-17, September.
    9. Sebastian Sager & Clemens Zeile, 2021. "On mixed-integer optimal control with constrained total variation of the integer control," Computational Optimization and Applications, Springer, vol. 78(2), pages 575-623, March.
    10. K. H. Wong & H. W. J. Lee & C. K. Chan & C. Myburgh, 2013. "Control Parametrization and Finite Element Method for Controlling Multi-species Reactive Transport in an Underground Channel," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 168-187, April.
    11. G. Vossen, 2010. "Switching Time Optimization for Bang-Bang and Singular Controls," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 409-429, February.
    12. Nahid Banihashemi & C. Yalçın Kaya, 2013. "Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 726-760, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0306-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.