Multi-Objective Controller Design using a Rank-Constrained Linear Matrix Inequality Method

계수조건부 LMI를 이용한 다목적 제어기 설계

  • Published : 2009.01.01


This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as $H_2/H_{\infty}$ control. Multi-objective control is formulated as an LMI optimization problem with a nonconvex rank condition, which is imposed on the controller gain matirx not Lyapunov matrices. With this rank-constrained formulation, we can expect to reduce conservatism because we can use separate Lyapunov matrices for different control objectives. An iterative penalty method is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method.


  1. D. s. Bernstein and W. M Haddad, "LQG control with an Hoo performance bound: a Riccatti equation approach,"IEEE Trans. Automatic Control, vo!. 34, no. 3, pp. 291-305, 1989
  2. P.P.KhargonekarandM.A.Rotea,"MixedH21H00control:aconvexoptimizationapproach," IEEE Trans.Automatic Control, vo!. 36, no. 7, pp. 824-837, 1991
  3. C. W. Scherer, P. Gahinet and M. Chilali,"Multiobjective output-feedback control via LMI optimization,"IEEE Trans. Automatic Control, vo!. 42, no.7, pp. 896-911, 1997
  4. F. Leibfiitz, "An LMI-based algorithm for designing suboptimal static H~oo output feedback controllers," SIAM J Control and Optimization, vo!. 39, no. 6, pp.1711-1735, 2001
  5. D. Arzelier and D. Peaucelle, "An iterative method for mixed H2IHoo synthesis via static output feedback," Proc.IEEE Con! Decision and Control, pp. 3644-3469, 2002
  6. T. Shimomura and T. Fuji, "An iterative method for mixed H2/R" control design with Wlcommon LMI solutions,"Proc. American Control Con! pp. 3292-3296,1999
  7. D. Peaucelle and D. Arzelier, "Ellipsoidal output-feed-back sets for robust multi-performance synthesis," Proc. European Control Conf. 2003
  8. P. Apkarian, D. Noli, and A. Rondepierre, "Mixed HiHoo control via nonsmooth optimization," SIAM J Control and Optimization, vol. 47, no. 3, pp. 1516-1546, 2008
  9. S. J. Kim, YOWlg-HyWl Moon, and Soonman Kwon, "Simultaneous stabilization by static output feedback: a rank constrained LMIapproach,"InProc.CorlfDecision and Control, pp. 5162-5167, 2006
  10. S. J. Kim and Y. H. Moon, "Structurally constrained H2 and H." control; A rank-constrained I,MI approach," Automatica, vol. 42, no. 9, pp. 1583-1588, 2006
  11. 김석주, 권순만, 천종민, 문영현 "페널티화된 LMI를이용한 구조적 제약이 있는 제어기 설계", 제어 • 자동화• 시스템공학 논문지, 제 11권 제8후 pp‘ 656-661, 2005
  12. J. F. Sturm, "Using SEDUMI 1.02, a MATLAB toolbox for optimization over syn1ITIetric cones," Available from http;
  13. J. Lotberg, "Y ALMIP 3," Available from