Advertisement

Multi-objective bounded control of uncertain nonlinear systems: an inverted pendulum example

  • Stéphane Dussy
  • Laurent El Ghaoui
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 227)

Keywords

Linear Matrix Inequality Inverted Pendulum Uncertain System Uncertain Nonlinear System Bound Input 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Apkarian, P. Gahinet, and G. Becker. Self-scheduled H control of linear parameter-varying systems: a design example. Automatica, 31(9):1251–1261, September 1995.CrossRefGoogle Scholar
  2. 2.
    V. Balakrishnan. Linear Matrix Inequalities in robustness analysis with multipliers. Syst. & Contr. Letters, 25(4):265–272, July 1995.Google Scholar
  3. 3.
    G. Becker and A. Packard. Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback. Syst. & Contr. Letters, 23(3):205–215, September 1994.Google Scholar
  4. 4.
    B. Bodenheimer and P. Bendotti. Optimal linear parameter-varying control design for a pressurized water reactor. In Proc. IEEE Conf. on Decision & Contr., pages 182–187, New Orleans, LA, December 1995.Google Scholar
  5. 5.
    S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequality in systems and control theory. SIAM, 1994.Google Scholar
  6. 6.
    J.C. Doyle, A. Packard, and K. Zhou. Review of LFTs, LMIs and μ. In Proc. IEEE Conf. on Decision & Contr., pages 1227–1232, Brignton, England, December 1991.Google Scholar
  7. 7.
    S. Dussy and L. El Ghaoui. Multiobjective Robust Control Toolbox (MRCT): user's guide, 1996. Available via http://www.ensta.fr/∼gropco/staff/dussy/gocpage.html.Google Scholar
  8. 8.
    S. Dussy and L. El Ghaoui. Robust gain-scheduled control of a class of nonlinear parameter-dependent systems: application to an uncertain inverted pendulum. In Proc. Conf. on Contr. & Applications, pages 516–521, Dearborn, MI, September 1996.Google Scholar
  9. 9.
    S. Dussy and L. El Ghaoui. Multiobjective Robust Control Toolbox for LMI-based control. In Proc. IFAC Symposium on Computer Aided Control Systems Design, Gent, Belgium, April 1997.Google Scholar
  10. 10.
    L. El Ghaoui, R. Nikoukhah, and F. Delebecque. LMITOOL: A front-end for LMI optimization, user's guide, February 1995. Available via anonymous ftp to ftp.ensta.fr, under /pub/elghaoui/lmitool.Google Scholar
  11. 11.
    L. El Ghaoui, F. Oustry, and M. Ait Rami. An LMI-based linearization algorithm for static output-feedback and related problems. IEEE Trans. Aut. Contr., May 1997.Google Scholar
  12. 12.
    L. El Ghaoui and G. Scorletti. Control of rational systems using Linear-Fractional Representations and Linear Matrix Inequalities. Automatica, 32(9):1273–1284, September 1996.CrossRefGoogle Scholar
  13. 13.
    T. Iwasaki and R.E. Skelton. All controllers for the general H control problems: LMI existence conditions and state space formulas. Automatica, 30(8):1307–1317, August 1994.CrossRefGoogle Scholar
  14. 14.
    A. Megretski and A. Rantzer. System analysis via integral quadratic constraints. In Proc. IEEE Conf. on Decision & Contr., pages 3062–3067, Orlando, FL, December 1994.Google Scholar
  15. 15.
    Y. Nesterov and A. Nemirovsky. Interior point polynomial methods in convex programming: theory and applications. SIAM, 1993.Google Scholar
  16. 16.
    A. Packard. Gain scheduling via Linear-Fractional Transformations. Syst. & Contr. Letters, 22(2):79–92, February 1994.Google Scholar
  17. 17.
    A. Packard, K. Zhou, P. Pandey, and G. Becker. A collection of robust control problems leading to LMI's. In Proc. IEEE Conf. on Decision & Contr., pages 1245–1250, Brighton, England, December 1991.Google Scholar
  18. 18.
    G. Scorletti and L. El Ghaoui. Improved Linear Matrix Inequalities conditions for gain-scheduling. In Proc. IEEE Conf. on Decision & Contr., pages 3626–3631, New Orleans, LA, December 1995.Google Scholar
  19. 19.
    L. Vandenberghe and S. Boyd. SP, Software for semidefinite programming, user's guide, December 1994. Available via anonymous ftp to isl.stanford.edu under /pub/boyd/semidef prog.Google Scholar

Copyright information

© Springer-Verlag London Limited 1997

Authors and Affiliations

  • Stéphane Dussy
    • 1
  • Laurent El Ghaoui
    • 1
  1. 1.Laboratoire de Mathématiques AppliquéesEcole Nationale Supérieure de Techniques AvançéesParisFrance

Personalised recommendations