선형행렬부등식을 이용한 정적출력궤환 제어기 설계

Design of a Static Output Feedback Stabilization Controller by Solving a Rank-constrained LMI Problem

  • 발행 : 2004.11.01

초록

This paper presents an iterative linear matrix inequality (LMI) approach to the design of a static output feedback (SOF) stabilization controller. A linear penalty function is incorporated into the objective function for the non-convex rank constraint so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. Hence, the overall procedure results in solving a series of semidefinite programs (SDPs). With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Extensive numerical experiments are Deformed to illustrate the proposed algorithm.

키워드

참고문헌

  1. Y. L. Syrmos, C. T. Abdallah, P. Dorate and K. Grigoriadis, 'Static output feedback - a survey', Automatica, Vol. 33, No. 1, pp. 125-137, 1997 https://doi.org/10.1016/S0005-1098(96)00141-0
  2. M. Mesbahi, 'A semi-definite programming solution of the least order dynamic output feedback synthesis problem', In Proc. of the IEEE Conf. on Decision and Control, pp. 1851-1856, 1999 https://doi.org/10.1109/CDC.1999.830903
  3. K. C. Goh, M. G. Safonov and G. P. Papavassilopoulos, 'A global optimization approach for the BMI problem', In Proc. IEEE Conf. on Decision and Control, pp. 2009-2114, 1994 https://doi.org/10.1109/CDC.1994.411445
  4. J. C. Geromel, C. C. de Souza and R. E. Skelton, 'LMI numerical solution for output feedback stabilization', In Proc. of the American Control Conference, pp. 40-44, 1994 https://doi.org/10.1109/ACC.1994.751689
  5. T. Iwasaki and R. E. Skelton, 'The XY-centering algorithm for the dual LMI problem: a new approach to fixed order control design', International Journal of Control, Vol. 62, No.6, pp. 1257-1272, 1995 https://doi.org/10.1080/00207179508921598
  6. K. M. Grigoriadis and R. E. Skelton, 'Low order control design for LMI problems using alternating projection methods', Automatica, Vol. 32, No. 8, pp, ?1117-1125, 1996 https://doi.org/10.1016/0005-1098(96)00057-X
  7. T. Iwasaki, 'The dual iteration for fixed order control', IEEE Trans. on Automatic Control, Vol. 44, No.4, pp.783-788, 1999 https://doi.org/10.1109/9.754818
  8. L. El Ghaoui, F. Oustry and M. Rami, 'A cone complementarity linearization algorithm for static output feedback and related problems', IEEE Trans. on Automatic Control, Vol. 42, No.8, 1171-1176, 1997 https://doi.org/10.1109/9.618250
  9. M. C. de Oliveira and J. C. Geromel, 'Numerical comparison of output feedback design methods', In Proc. of the American Control Conference, pp. 72-76, 1997 https://doi.org/10.1109/ACC.1997.611757
  10. Y. Y. Cao, L. James and Y. X. Sun, 'Static output feedback stabilization: ILMI approach', Automatica, Vol. 34, No. 12, pp. 1641-1645, 1998 https://doi.org/10.1016/S0005-1098(98)80021-6
  11. M. Fazel H. Hindi and S. Boyd, 'Log-det heuristic for matrix rank minimization with application to Hankel and euclidean distance matrices', In Proc. of the American Control Conference, pp. 2156-2162, 2003 https://doi.org/10.1109/ACC.2003.1243393
  12. R. A. Horn and C. R. Johnson, 'Matrix Analysis', Cambridge University Press, 1986
  13. D. G. Luenberger, 'Linear and Nonlinear Programming', Addison-Wesley, 1982
  14. J. F. Sturm, 'Using SEDUMI 1.02, a MATLAB toolbox for optimization over symmetric cones', Available from http://fewcal.kub.nl/-sturm
  15. J. Lofberg, 'YALMIP 3', Available from http://control.ee.ethz.ch/-joloef
  16. D. Noll, M. Torki and P. Apkarian, 'Partially augmented Lagrangian method for matrix inequalities constraints', Preprint, Available from http://wwwext.cert.fr/dcsd/cdin/apkarian