Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2012 | 22 | 2 | 353-363
Tytuł artykułu

An SQP trust region method for solving the discrete-time linear quadratic control problem

Treść / Zawartość
Warianty tytułu
Języki publikacji
In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution to initiate the proposed SQP trust region method. To demonstrate the effectiveness of the method, some numerical results are presented in detail.
Opis fizyczny
  • Department of Mathematics, Faculty of Science, Alexandria University, Moharam Bey, 21511, Alexandria, Egypt
  • Conn, A.R., Gould, N.I.M. and Toint, Ph.L. (2000). TrustRegion Methods, SIAM, Philadelphia, PA.
  • Garcia, G., Pradin, B. and Zeng, F. (2001). Stabilization of discrete-time linear systems by static output feedback, IEEE Transactions on Automatic Control 46(12): 1954-1958.
  • Kočvara M., Leibfritz, F., Stingl, M. and Henrion, D. (2005). A nonlinear SDP algorithm for static output feedback problems in COMPlib, Proceedings of the 16th IFAC World Congress on Automatic Control, Prague, Czech Republic, (on CDROM).
  • Lee, J.-W. and Khargonekar, P.P. (2007). Constrained infinitehorizon linear quadratic regulation of discrete-time systems, IEEE Transactions on Automatic Control 52(10): 1951-1958.
  • Leibfritz, F. (2004). COMPlib: COnstraint Matrixoptimization Problem library-A collection of test examples for nonlinear semi-definite programs, control system design and related problems, Technical report,
  • Leibfritz, F. and Mostafa, E.M.E. (2002). An interior point constrained trust region method for a special class of nonlinear semidefinite programming problems, SIAM Journal on Optimization 12(4): 1048-1074.
  • Leibfritz, F. and Mostafa, E.M.E. (2003). Trust region methods for solving the optimal output feedback design problem, International Journal of Control 76(5): 501-519.
  • Mäkilä, P.M. and Toivonen, H.T. (1987). Computational methods for parametric LQ problems-A survey, IEEE Transactions on Automatic Control 32(8): 658-671.
  • Mostafa, E.M.E. (2005a). A trust region method for solving the decentralized static output feedback design problem, Journal of Applied Mathematics & Computing 18(1-2): 1-23.
  • Mostafa, E.M.E. (2005b). An augmented Lagrangian SQP method for solving some special class of nonlinear semidefinite programming problems, Computational and Applied Mathematics 24(3): 461-486.
  • Mostafa, E.M.E. (2008). Computational design of optimal discrete-time output feedback controllers, Journal of the Operations Research Society of Japan 51(1): 15-28.
  • Mostafa, E.M.E. (2012). A conjugate gradient method for discrete-time output feedback control design, Journal of Computational Mathematics 30(3): 279-297.
  • Nocedal J. and Wright, S.J. (1999). Numerical Optimization, Springer, New York, NY.
  • Peres, P.L.D. and Geromel, J.C. (1993). H₂ control for discretetime systems optimality and robustness, Automatica 29(1): 225-228.
  • Sulikowski, B., Gałkowski, K., Rogers, E. and Owens, D.H. (2004). Output feedback control of discrete linear repetitive processes, Automatica 40(12): 2167-2173.
  • Syrmos, V.L., Abdallah, C.T., Dorato, P. and Grigoriadis, K. (1997). Static output feedback-A survey, Automatica 33(2): 125-137.
  • Varga, A. and Pieters, S. (1998). Gradient-based approach to solve optimal periodic output feedback control problems, Automatica 34(4): 477-481.
  • Zhai, G., Matsumoto, Y., Chen, X., Imae, J. and Kobayashi, T. (2005). Hybrid stabilization of discrete-time LTI systems with two quantized signals, International Journal of Applied Mathematics and Computer Science 15(4): 509-516. El-Sayed M.E. Mostafa received the B.Sc. degree in mathematics from Alexandria University, Egypt, in 1989, the M.Sc. degree in industrial mathematics from the University of Kaisersluatern, Germany, in 1994, and the Ph.D. degree in numerical optimization from Alexandria University in 2000. Since 2008 he has been working as an associate professor at the Department of Mathematics, Faculty of Science, Alexandria University. His research interests include numerical optimization and optimal control with engineering applications.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.