Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 638762, 14 pages
http://dx.doi.org/10.1155/2012/638762
Research Article

Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods

College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China

Received 10 August 2011; Accepted 4 December 2011

Academic Editor: Oluwole D. Makinde

Copyright © 2012 Shaowei Zhou and Weihai Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. M. Wonham, “On a matrix Riccati equation of stochastic control,” SIAM Journal on Control and Optimization, vol. 6, no. 4, pp. 681–697, 1968. View at Google Scholar
  2. C. E. De Souza and M. D. Fragoso, “On the existence of maximal solution for generalized algebraic Riccati equations arising in stochastic control,” Systems & Control Letters, vol. 14, no. 3, pp. 233–239, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. P. J. McLane, “Optimal stochastic control of linear systems with state- and control-dependent disturbances,” IEEE Transactions on Automatic Control, vol. 16, no. 6, pp. 793–798, 1971. View at Publisher · View at Google Scholar
  4. W. H. Zhang and B. S. Chen, “On stabilizability and exact observability of stochastic systems with their applications,” Automatica, vol. 40, no. 1, pp. 87–94, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. W. H. Zhang, H. S. Zhang, and B. S. Chen, “Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion,” IEEE Transactions on Automatic Control, vol. 53, no. 7, pp. 1630–1642, 2008. View at Publisher · View at Google Scholar
  6. F. Carravetta and G. Mavelli, “Suboptimal stochastic linear feedback control of linear systems with state- and control-dependent noise: the incomplete information case,” Automatica, vol. 43, no. 5, pp. 751–757, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Springer, Berlin, Germany, 1975.
  8. M. H. A. Davis, Linear Estimation and Stochastic Control, Chapman and Hall, London, UK, 1977, Chapman and Hall Mathematics Serie.
  9. S. P. Chen, X. J. Li, and X. Y. Zhou, “Stochastic linear quadratic regulators with indefinite control weight costs,” SIAM Journal on Control and Optimization, vol. 36, no. 5, pp. 1685–1702, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. A. Rami, X. Chen, J. B. Moore, and X. Y. Zhou, “Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls,” IEEE Transactions on Automatic Control, vol. 46, no. 3, pp. 428–440, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. M. A. Rami and X. Y. Zhou, “Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls,” IEEE Transactions on Automatic Control, vol. 45, no. 6, pp. 1131–1143, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. M. A. Rami, J. B. Moore, and X. Y. Zhou, “Indefinite stochastic linear quadratic control and generalized differential Riccati equation,” SIAM Journal on Control and Optimization, vol. 40, no. 4, pp. 1296–1311, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. X. Li, X. Y. Zhou, and M. A. Rami, “Indefinite stochastic linear quadratic control with Markovian jumps in infinite time horizon,” Journal of Global Optimization, vol. 27, no. 2-3, pp. 149–175, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. X. Li and X. Y. Zhou, “Indefinite stochastic LQ controls with Markovian jumps in a finite time horizon,” Communications in Information and Systems, vol. 2, no. 3, pp. 265–282, 2002. View at Google Scholar · View at Zentralblatt MATH
  15. M. A. Rami, X. Chen, and X. Y. Zhou, “Discrete-time indefinite LQ control with state and control dependent noises,” Journal of Global Optimization, vol. 23, no. 3-4, pp. 245–265, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. J. J. Qi and W. H. Zhang, “Discrete-time indefinite stochastic LQ optimal control: infinite horizon case,” Acta Automatica Sinica, vol. 35, no. 5, pp. 613–617, 2009. View at Google Scholar
  17. Y. L. Huang, W. H. Zhang, and H. S. Zhang, “Infinite horizon linear quadratic optimal control for discrete-time stochastic systems,” Asian Journal of Control, vol. 10, no. 5, pp. 608–615, 2008. View at Publisher · View at Google Scholar
  18. D. D. Yao, S. Zhang, and X. Y. Zhou, “Stochastic linear-quadratic control via semidefinite programming,” SIAM Journal on Control and Optimization, vol. 40, no. 3, pp. 801–823, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. V. Balakrishnan and L. Vandenberghe, “Semidefinite programming duality and linear time-invariant systems,” IEEE Transactions on Automatic Control, vol. 48, no. 1, pp. 30–41, 2003. View at Publisher · View at Google Scholar
  20. L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Review, vol. 38, no. 1, pp. 49–95, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. A. El Bouhtouri, D. Hinrichsen, and A. J. Pritchard, “H-type control for discrete-time stochastic systems,” International Journal of Robust and Nonlinear Control, vol. 9, no. 13, pp. 923–948, 1999. View at Google Scholar · View at Zentralblatt MATH
  22. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994.