Skip to main content

Advertisement

SpringerLink
Log in

New Robust Model Predictive Control for Uncertain Systems with Input Constraints Using Relaxation Matrices

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, we propose a new robust model predictive control (MPC) method for time-varying uncertain systems with input constraints. We formulate the problem as a minimization of the worst-case finite-horizon cost function subject to a new sufficient condition for cost monotonicity. The proposed MPC technique uses relaxation matrices to derive a less conservative terminal inequality condition. The relaxation matrices improve feasibility and system performance. The optimization problem is solved by semidefinite programming involving linear matrix inequalities (LMIs). A numerical example shows the effectiveness of the proposed method.

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. Kothare, M.V., Balakrishanan, V., Morari, M.: Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10), 1361–1379 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cuzzola, F.A., Geromel, J.C., Morari, M.: An improved approach for constrained robust model predictive control. Automatica 38, 1183–1189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Mao, W.: Robust stabilization of uncertain time-varying discrete systems and comments on “An improved approach for constrained robust model predictive control”. Automatica 39, 1109–1112 (2003)

    Article  MATH  Google Scholar 

  4. Ding, B., Xi, Y., Li, S.: A synthesis approach of on-line constrained robust model predictive control. Automatica 40, 163–167 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Casavola, A., Famularo, D., Franze, G.: Robust constrained predictive control of uncertain norm-bounded linear systems. Automatica 40, 1865–1876 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kim, K.B.: Implementation of stabilizing receding horizon controls. Automatica 38, 1705–1711 (2002)

    Article  MATH  Google Scholar 

  7. Rawlings, J.B., Muske, K.R.: The stability of constrained receding horizon control. IEEE Trans. Autom. Control 38, 1512–1516 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lee, J.W., Kwon, W.H., Choi, J.H.: On stability of constrained receding horizon control with finite terminal weighting matrix. Automatica 34, 1607–1612 (1998)

    Article  MATH  Google Scholar 

  9. Boyd, S., Ghaoui, L., Feron, E., Balakrishanan, V.: Linear Matrix Inequalities in System and Control Theory. Studies in Applied Mathematics, vol. 15. SIAM, Philadelphia (1994)

    MATH  Google Scholar 

  10. Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. Mathworks, Natick (1995)

    Google Scholar 

  11. Casavola, A., Mosca, E.: A correction to min-max predictive control strategies for input-saturated polytopic uncertain systems. Automatica 43, 384–385 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Pluymers, B.: Robust model based predictive control—an invariant set approach. PhD thesis, Faculty of Engineering, K.U. Leuven, Leuven, Belgium, May 2006

Download references

Author information

Authors and Affiliations

  1. Platform Verification Division, BcN Business Unit, KT Co. Ltd., Daejeon, Republic of Korea

    S. M. Lee

  2. Department of Electronic and Electrical Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea

    S. C. Won

  3. Department of Electrical Engineering, Yeungnam University, Kyongsan, Republic of Korea

    J. H. Park

Authors
  1. S. M. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. C. Won
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. H. Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. H. Park.

Additional information

Communicated by M. Corless.

The authors thank the associate editor and two anonymous referees for careful reading and useful suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, S.M., Won, S.C. & Park, J.H. New Robust Model Predictive Control for Uncertain Systems with Input Constraints Using Relaxation Matrices. J Optim Theory Appl 138, 221–234 (2008). https://doi.org/10.1007/s10957-008-9375-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-008-9375-5

Keywords

Search

Navigation