Skip to main content
SpringerLink
Log in

Application of nonlinear rescaling method to model predictive control

  • Regular Papers
  • Control Theory
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, we present the application of a nonlinear rescaling method for an efficient solution to the constrained optimal control problem in model predictive control. A smooth scaling function is used to transform the constraints to a sequential unconstrained optimization problem. Simulation results demonstrate the effectiveness of this approach with regards to model predictive controller with saturation.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Meadows and J. Rawlings, Nonlinear Process Control, Chapter: Model predictive control, pp. 233–310, Prentice-Hall, Upper Saddle River, NJ, 1997.

    Google Scholar 

  2. D. W. Clarke, C. Mohtadi, and P. S. Tuffs, “Generalized predictive control, part I: the basic algorithm, part II: extension and interpretation,” Automatica, vol. 32, pp. 137–160, 1987.

    Article  Google Scholar 

  3. E. F. Camacho and C. Bordons, Model Predictive Control, 2nd ed., Springer-Verlag, London, 2004.

    MATH  Google Scholar 

  4. D. P. Bertsekas, Dynamic Programming, Prentice-Hall, Englewood Cliffs, New Jersey, 1987.

    MATH  Google Scholar 

  5. L. Chisci and G. Zappa, “Fast QP algorithms for predictive control,” Proc. of the 38th Conference On Decision and Control, Phoenix, Arizona, USA, Dec. 1999.

  6. S. G. Nash, R. A. Polyak, and A. Sofer, “Numerical comparison of barrier and modified-barrier methods for large scale bound-constrained optimization, large scale optimization: state of the art,” Kluwer Academic Publishers, pp. 319–338, 1994.

  7. E. Polak, T. H. Yang, and D. Q. Mayne, “A method of centre based on barrier functions for solving optimal control problems with continuous state and constraints,” Proc. of the 29th Conference On Decision and Control, Hawaii, vol. 4 pp. 2327, 1990.

    Article  Google Scholar 

  8. A. G. Wills and W. P. Heath, “Barrier function based model predictive control,” Automatica, vol. 40, pp. 1415–1422, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Hamdi, “Decomposition for structured convex programs with smooth multiplier methods,” Applied Mathematics and Computation, vol. 169, pp. 218–241, 2004.

    Article  MathSciNet  Google Scholar 

  10. R. A. Polyak and M. Teboulle, “Nonlinear rescaling and proximal-like methods in convex optimization,” Mathematical Programming, vol. 76, pp. 265–284, 1997.

    MathSciNet  Google Scholar 

  11. R. A. Polyak, “Nonlinear rescaling vs. smoothing technique in convex optimization,” Math. Program. Ser. A, vol. 92, pp. 197–235, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. A. Polyak, “Modified barrier functions: theory and methods,” Mathematical Programming, vol. 54, pp. 177–222, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Atkinson and W. Han, Theoretical Numerical Analysis: A Function Analysis Framework, 3rd Edition, Springer-Verlag, 2009.

  14. G. C. Goodwin, M. M. Seron, and J. A. De Donà, Constrained Control and Estimation: An Optimization Approach, Spriger-Verlag, London, 2005.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Engineering Department, College of Computer and Information Sciences-King Saud University, P.O.Box 51178, Riyadh, 11543, Kingdom of Saudi Arabia

    Ramdane Hedjar

Authors
  1. Ramdane Hedjar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ramdane Hedjar.

Additional information

Recommended by Editorial Board member Kwang Soon Lee under the direction of Editor Young IL Lee.

Ramdane Hedjar received the B.Sc. and Ph.D. degrees from USTHB University, Algiers, in 1988 and 2002 respectively and his M.Sc. degree from BLIDA University in Algeria. After finishing the Ph.D. degree, he joined the Computer Engineering Department at King Saud University as an assistant professor. From 1992 to 2000, he was a lecturer in Electronics Department at Djelfa University. Currently, Dr. Hedjar is an associate professor in the Computer Engineering Department at King Saud University. His research interests include robust control, nonlinear predictive control, robotics, neural network control, and Networked control systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hedjar, R. Application of nonlinear rescaling method to model predictive control. Int. J. Control Autom. Syst. 8, 762–768 (2010). https://doi.org/10.1007/s12555-010-0407-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-010-0407-1

Keywords

Search

Navigation