Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2007.13.11.1048

Rank-constrained LMI Approach to Simultaneous Linear Quadratic Optimal Control Design  

Kim, Seog-Joo (한국전기연구원계측제어그룹)
Cheon, Jong-Min (한국전기연구원계측제어그룹)
Kim, Jong-Moon (한국전기연구원계측제어그룹)
Kim, Chun-Kyung (한국전기연구원계측제어그룹)
Lee, Jong-Moo (한국전기연구원계측제어그룹)
Kwon, Soom-Nam (한국전기연구원계측제어그룹)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.13, no.11, 2007 , pp. 1048-1052 More about this Journal
Abstract
This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.
Keywords
Linear Matrix Inequality(LMI); static output feedback(SOF); penalty function method; simultaneous stabilization; LQ optimal control;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. Lofberg, 'YALMIP 3,' Available from http://control.ee.ethz.ch/~joloef
2 V. D. Blondel and J. N. Tsitsiklis, 'A survey of computational complexity results in systems and control,' Automatica, vol. 36, no. 9, pp. 1249-1274, 2000   DOI   ScienceOn
3 J. Lam and Y. Y. Cao, 'Simultaneous linear-quadratic optimal control design via static output feedback,' Int. J. Robust and Nonlinear Control, vol. 9, pp. 551-558, 1999   DOI   ScienceOn
4 R. A. Luke, P. Dorato, and C. T. Abdallah, 'Linear-quadratic simultaneous performance design,' In Proc. Amer. Control Conf., pp. 3602-3605, 1997
5 Y. He and Q.,-G. Wang, 'An improved ILMI method for static output feedback control with application to multivariable PID control,' IEEE Trans. Automatic Control, vol. 51, no. 10, pp. 1678-1683, 2006   DOI   ScienceOn
6 P. Apkarian and D. Noll, 'Nonsmooth $H_{\infty}$ synthesis,' IEEE Trans. Automatic Control, vol. 51, no. 1, pp. 71-86, 2006   DOI   ScienceOn
7 S. J. Kim, Y.-H. Moon, and S. M. Kwon, 'Simultaneous stabilization by static output feedback: a rank constrained LMI approach,' In Proc. Conf. Decision and Control, pp. 5162-5167, 2006
8 S. J. Kim, Y. H. Moon, S. Kwon, and K. H. Kim, 'Rank-constrained LMI approach to mixed $H_{2}$/$H_{\infty}$ static ouptut feedback controllers,' Preprints of the 16th IFAC World congress, 2005
9 S. J. Kim and Y. H. Moon, 'Structurally constrained $H_{2}$ and $H_{\infty}$, control: A rank-constrained LMI approach,' Automatica, vol. 42, no. 9, pp. 1583-1588, 2006   DOI   ScienceOn
10 J. F. Sturm, 'Using SEDUMI 1.02, a MATLAB toolbox for optimization over symmetric cones,' Available from http://fewcal.kub.nl/~sturm
11 P. Apkarian and D. Noll, 'Controller design via nonsmooth multi-directional search,' SIAM J. on Control and Optimization, vol. 44, no. 6, pp. 1923-1949, 2006   DOI   ScienceOn