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Robust Model Predictive Control Using Polytopic Description of Input Constraints

  • Published : 2009.12.01

Abstract

In this paper, we propose a less conservative a linear matrix inequality (LMI) condition for the constrained robust model predictive control of systems with input constraints and polytopic uncertainty. Systems with input constraints are represented as perturbed systems with sector bounded conditions. For the infinite horizon control, closed-loop stability conditions are obtained by using a parameter dependent Lyapunov function. The effectiveness of the proposed method is shown by an example.

Keywords

References

  1. M. V. Kothare, V. Balakrishanan, and M. Morari, ' Robust constrained model predictive control using linear matrix inequalitiεs,' Automatica, vol. 32., no. 10, pp. 1361-1379, 1996 https://doi.org/10.1016/0005-1098(96)00063-5
  2. F. A., Cuzzola, J. C. Geromel , and M. Morari, 'An improvεd approach for constrainεd robust model predictive control,' Automatica, vol. 38., pp. 1183-1189, 2002 https://doi.org/10.1016/S0005-1098(02)00012-2
  3. 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 https://doi.org/10.1016/j.automatica.2003.07.007
  4. A. Casavola, D. Famularo, and G. Franzε, ' Robust constrained predictive control of uncertain normbounded linear systems,' Automatica, vol, 40, pp.1865-1876, 2004 https://doi.org/10.1016/j.automatica.2004.05.016
  5. K. B. Kim, 'Implεmentation of stabilizing receding horizon controls,' Automatica, vol. 38, pp. 1705-1711 , 2002 https://doi.org/10.1016/S0005-1098(02)00087-0
  6. J. B. Rawlings, and K. R. Muskε, ' The stability of constrained receding horizon control,' IEEE Transactions on Automatic Control, vol. 38, pp. 1512-1516,1993 https://doi.org/10.1109/9.241565
  7. J. W. Lee, W. H. Kwon, and J. H. Choi,, 'On stability of constrainεd receding horizon control with finitε terminal weighting matrix,' Automatica, vol. 34, pp.1607-1612, 1998 https://doi.org/10.1016/S0005-1098(98)80015-0
  8. S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishanan, ' Linear matrix inεqualities in system and control theory,' Studies in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, vol. 15, 1994
  9. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI control toolbox, The Mathworks, Natick, Massachusetts, 1995
  10. S. M. Lee, S. C. Won, and J. H. Park, 'New Robust Model Predictive Control for Uncεrtain Systems with Input Constraints Using Relaxation Matrices,' Journal of Optimization Theon and Applications, 138, pp. 221-234, 2008 https://doi.org/10.1007/s10957-008-9375-5
  11. S. M. Lee, and S. C. Won, ' Robust constrained predictive control using a sεctor bounded nonlinear model,' IET Control Theory Appl., 1, (4), pp. 999-1007, 2007 https://doi.org/10.1049/iet-cta:20060203
  12. S. M. Lee, 1. H. Park, D. H. Ji, and S. C. Won, Robust model prεdictive control for LPV systems using relaxation matrices, IET Control Theon Appl., 1, (6), pp.1567-1573, 2007 https://doi.org/10.1049/iet-cta:20060525