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Robust multi-model predictive control using LMIs

  • Paola Falugi
  • Sorin OlaruEmail author
  • Didier Dumur
Technical Notes and Correspondence

Abstract

This paper proposes a novel synthesis technique for robust predictive control of constrained nonlinear systems based on linear matrix inequalities (LMIs) formalism. Local discrete-time polytopic models are exploited for prediction of the system behavior. This design strategy can be applied to nonlinear systems provided a suitable embedding is available. The devised procedure guarantees constraint satisfaction and asymptotic stability. The proposed result extends previous works by handling less conservative input constraints and exploiting the different local descriptions of nonlinearity and uncertainty. The multi-model prediction together with the modified input constraints show significant improvements in terms of closed-loop performance and estimation of the feasibility domain.

Keywords

Control of constrained nonlinear systems LMIs model predictive control 

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References

  1. [1]
    M. Bacic, M. Cannon, and B. Kouvaritakis, “Extension of efficient predictive control to the nonlinear case,” Int. Journal of Robust and Nonlinear Control, vol. 15, no. 5, pp. 219–231, 2005.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    A. Ben-Tal and A. Nemirovski, Editors, Lectures on Modern Convex Optimization, MPS-SIAM Series on Optimization, 2001.Google Scholar
  3. [3]
    F. Blanchini and S. Miani, Set-Theoretic Methods in Control (Systems & Control: Foundations & Applications), Birkhauser, Boston, USA, 2007.Google Scholar
  4. [4]
    S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, USA, 1994.zbMATHGoogle Scholar
  5. [5]
    J. M. Bravo, D. Limon, T. Alamo, and E. F. Camacho, “On the computation of invariant sets for constrained nonlinear systems: an interval arithmetic approach,” Automatica, vol. 41, pp. 1583–1589, 2005.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    L. Chisci, P. Falugi, and G. Zappa, “Gain-scheduling mpc control of nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 13, pp. 295–308, 2003.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    F. A. Cuzzola and M. Morari, “A generalized approach for analysis and control of discrete-time piecewise affine and hybrid systems,” Proc. of International Workshop on Hybrid Systems: Computation and Control, pp. 189–203, Roma, Italy, 2001.Google Scholar
  8. [8]
    B. Ding, Y. Xi, and S. Li, “A synthesis approach of on-line constrained robust model predictive control,” Automatica, vol. 40, pp. 163–167, 2004.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    G. C. Goodwin, M. M. Seron, and J. A. De Dona, Editors, Constrained Control and Estimation, Springer-Verlag, London, UK, 2004.Google Scholar
  10. [10]
    P. J. Goulart and E. C. Kerrigan, “A method for robust receding horizon output feedback control of constrained systems,” Proc. of the 45th IEEE CDC, San Diego, CA, USA, 2006.Google Scholar
  11. [11]
    A. Hassibi, J. How, and S. Boyd, “A pathfollowing method for solving bmi problems in control,” Proc. of American control conference, pp. 1385–1389, San Diego, California, USA, 1999.Google Scholar
  12. [12]
    M. V. Kothare, V. Balakrishnan, and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, no. 10, pp. 1361–1379, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    M. Lazar, W. P. M. H. Heemels, S. Weiland, and A. Bemporad, “On the stability of quadratic forms based model predictive control of constrained pwa systems,” Proc. of American Control Conference, pp. 575–580, Portland, OR, USA, 2005.Google Scholar
  14. [14]
    M. Lazar, W. P. M. H. Heemels, S. Weiland, and A. Bemporad, “Stabilizing model predictive control of hybrid systems,” Journal of Process Control, vol. 51, no. 11, pp. 1813–1818, 2006.MathSciNetGoogle Scholar
  15. [15]
    Y. I. Lee, M. Cannon, and B. Kouvaritakis, “Extended invariance and its use in model predictive control,” Automatica, vol. 41, pp. 2163–2169, 2005.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    Y. Lu and Y. Arkun, “A scheduling quasi-min-max model predictive control algorithm for nonlinear systems,” Journal of Process Control, vol. 12, no. 5, pp. 589–604, 2002.CrossRefGoogle Scholar
  17. [17]
    D. Q. Mayne, C. V. Rao, J. B. Rawlings, and P. O. M. Scokaert, “Constrained model predictive control: Stability and optimality,” Automatica, vol. 36, pp. 789–814, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    D. Q. Mayne and S. Rakovic, “Model predictive control of constrained pwa discrete-time systems,” International Journal of Robust and Nonlinear Control, vol. 13, pp. 261–279, 2003.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    D. Mignone, G. Ferrari-Trecate, and M. Morari, “Stability and stabilization of piecewise affine and hybrid systems: an LMI approach,” Proc. of IEEE Conference on Decision and Control, Sydney, Australia, 2000.Google Scholar
  20. [20]
    D. Muñoz de la Peña, A. Bemporad, and C. Filippi, “Robust explicit mpc based on approximate multiparametric convex programming,” IEEE Trans. on Automatic Control, vol. 51, pp. 1399–1403, 2006.CrossRefGoogle Scholar
  21. [21]
    L. Özkan, M. V. Kothare, and C. Georgakis, “Model predictive control of nonlinear systems using piecewise linear models,” Computers and Chemical Engineering, vol. 24, pp. 793–799, 2000.CrossRefGoogle Scholar
  22. [22]
    B. Pluymers, J. A. Rossiter, J. A. K. Suykens, and B. De Moor, “Interpolation based mpc for lpv systems using polyhedral invariant sets,” Proc. of American Control Conference, pp. 810–815, Portland, Oregon, USA, 2005.Google Scholar
  23. [23]
    W. J. Rugh and J. S. Shamma, “Research on gain scheduling,” Automatica, vol. 36, pp. 1401–1426, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  24. [24]
    E. D. Sontag, “Nonlinear regulation: the piecewise linear approach,” IEEE Trans. on Automatic Control, vol. 26, no. 2, pp. 346–358, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  25. [25]
    J. G. VanAntwerp and R. D. Braatz, “A tutorial on linear and bilinear matrix inequalities,” Journal of Process Control, vol. 10, pp. 363–385, 2000.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.SUPELEC, Automatic Control DepartmentPlateau de MoulonGif sur Yvette cedexFrance

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