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

Muhafzan

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 4, page 655-664
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Muhafzan. "Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems." International Journal of Applied Mathematics and Computer Science 20.4 (2010): 655-664. <http://eudml.org/doc/208014>.

@article{Muhafzan2010,
abstract = {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.},
author = {Muhafzan},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {rectangular descriptor system; LQR problem; restricted system equivalent; semidefinite programming},
language = {eng},
number = {4},
pages = {655-664},
title = {Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems},
url = {http://eudml.org/doc/208014},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Muhafzan
TI - Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 4
SP - 655
EP - 664
AB - 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.
LA - eng
KW - rectangular descriptor system; LQR problem; restricted system equivalent; semidefinite programming
UR - http://eudml.org/doc/208014
ER -

References

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  11. 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. Zbl0981.93080
  12. 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. Zbl1044.15014
  13. Vandenberghe, L. and Boyd, S. (1999). Applications of semidefinite programming, Applied Numerical Mathematics 29: 283-299. Zbl0956.90031
  14. 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. Zbl0994.49022

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