- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 674087, 14 pages
Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming
College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China
Received 19 October 2011; Accepted 29 November 2011
Academic Editor: Xue-Jun Xie
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.
- W. M. Wonham, “On a matrix Riccati equation of stochastic control,” SIAM Journal on Control, vol. 6, no. 4, pp. 681–697, 1968.
- C. E. de Souza and M. D. Fragoso, “On the existence of maximal solution for generalized algebraic Riccati equations arising in stochastic control,” Systems and Control Letters, vol. 14, no. 3, pp. 233–239, 1990.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- D. D. Yao, S. Z. 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.
- A. Beghi and D. D'Alessandro, “Discrete-time optimal control with control-dependent noise and generalized Riccati difference equations,” Automatica, vol. 34, no. 8, pp. 1031–1034, 1998.
- 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.
- 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.
- L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Review, vol. 38, no. 1, pp. 49–95, 1996.
- 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.
- A. El Bouhtouri, D. Hinrichsen, and A. J. Pritchard, “-type control for discrete-time stochastic systems,” International Journal of Robust and Nonlinear Control, vol. 9, no. 13, pp. 923–948, 1999.
- B. D. O. Anderson and J. B. Moore, Optimal Control-Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs, NJ, USA, 1989.