Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

Open access

Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

This paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.

Anderson, B. D. O. and Moore, J. B. (1990). Optimal Control: Linear Quadratic Methods, Prentice-Hall, Upper Saddle River, NJ.

Balakrishnan, V. and Vandenberghe, L. (2003). Semidefinite programming duality and linear time-invariant systems, IEEE Transactions on Automatic Control 48(1): 30-41.

Bender, D. J. and Laub, A. J. (1987). The linear quadratic optimal regulator for descriptor systems, IEEE Transactions on Automatic Control 32(8): 672-688.

Dai, L. (1989). Singular Control Systems, Lecture Notes in Control and Information Sciences, Vol. 118, Springer, Berlin.

Geerts, T. (1994). Linear quadratic control with and without stability subject to general implicit continuous time systems: Coordinate-free interpretations of the optimal cost in terms of dissipation inequality and linear matrix inequality, Linear Algebra and Its Applications 203-204: 607-658.

Ishihara, J. Y. and Terra, M. H. (2001). Impulse controllability and observability of rectangular descriptor systems, IEEE Transactions on Automatic Control 46: 991-994.

Jiandong, Z., Shuping, M. and Zhaolin, C. (2002). Singular LQ problem for nonregular descriptor system, IEEE Transactions on Automatic Control 47(7): 1128-1133.

Katayama, T. and Minamino, K. (1992). Linear quadratic regulator and spectral factorization for continuous time descriptor system, Proceedings of the IEEE Conference on Decision and Control, Tucson, AZ, USA, pp. 967-972.

Klema, V. C. and Laub, A. J. (1980). The singular value decomposition: Its computation and some applications IEEE Transactions on Automatic Control 25(2): 164-176.

Mehrmann, V. (1989). Existence, uniqueness, and stability of solutions to singular linear quadratic optimal control problems, Linear Algebra and Its Applications 121: 291-331.

Rami, M. A. and Zhou, X. Y. (2000). Linear matrix inequalities, riccati equations, and indefinite stochastic linear quadratic controls, IEEE Transactions on Automatic Control 45(6): 1131-1143.

Silva, M. S. and de Lima, T. P. (2003). Looking for nonnegative solutions of a leontif dynamic model, Linear Algebra and Its Applications 364: 281-316.

Vandenberghe, L. and Boyd, S. (1999). Applications of semidefinite programming, Applied Numerical Mathematics 29: 283-299.

Yao, D., Zhang, D. and Zhou, X. Y. (2001). A primal dual semidefinite programming approach to linear quadratic control, IEEE Transactions on Automatic Control 46(9): 1442-1447.

International Journal of Applied Mathematics and Computer Science

Journal of the University of Zielona Góra

Journal Information

IMPACT FACTOR 2018: 1,504
5-year IMPACT FACTOR: 1,553

CiteScore 2018: 2.09

SCImago Journal Rank (SJR) 2018: 0.493
Source Normalized Impact per Paper (SNIP) 2018: 1.361

Mathematical Citation Quotient (MCQ) 2017: 0.13

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 138 119 6
PDF Downloads 45 42 4