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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 7679165, 9 pages
http://dx.doi.org/10.1155/2016/7679165
Research Article

Optimal Preview Control for a Class of Linear Continuous Stochastic Control Systems in the Infinite Horizon

1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2Leeds Sustainability Institute, Leeds Beckett University, Leeds LS2 9EN, UK

Received 1 July 2016; Accepted 26 September 2016

Academic Editor: Andrzej Swierniak

Copyright © 2016 Jiang Wu et al. 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. M. Tomizuka, “Optimal continuous finite preview problem,” IEEE Transactions on Automatic Control, vol. 20, no. 3, pp. 362–365, 1975. View at Google Scholar · View at MathSciNet
  2. Y. Xu, F. Liao, L. Cui, and J. Wu, “Preview control for a class of linear continuous time-varying systems,” International Journal of Wavelets, Multiresolution and Information Processing, vol. 11, no. 2, Article ID 1350018, 1350018, 14 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. F. Liao, M. Cao, Z. Hu, and P. An, “Design of an optimal preview controller for linear discrete time causal descriptor systems,” International Journal of Control, vol. 85, no. 10, pp. 1616–1624, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. F. Liao, K. Takaba, T. Katayama, and J. Katsuura, “Design of an optimal preview servomechanism for discrete-time systems in a multirate setting,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms, vol. 10, no. 5, pp. 727–744, 2003. View at Google Scholar · View at MathSciNet
  5. T. Katayama, T. Ohki, T. Inoue, and T. Kato, “Design of an optimal controller for a discrete-time system subject to previewable demand,” International Journal of Control, vol. 41, no. 3, pp. 677–699, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. F. Liao, Y. Guo, and Y. Y. Tang, “Design of an optimal preview controller for linear time-varying discrete systems in a multirate setting,” International Journal of Wavelets, Multiresolution and Information Processing, vol. 13, no. 6, Article ID 1550050, 1550050, 19 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. T. Tsuchiya and T. Egami, Digital Preview and Predictive Control, Translated by Fucheng Liao, Beijing Science and Technology Press, Beijing, China, 1994.
  8. M. Cao and F. Liao, “Design of an optimal preview controller for linear discrete-time descriptor systems with state delay,” International Journal of Systems Science, vol. 46, no. 5, pp. 932–943, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Z. Y. Zhen, Z. S. Wang, and D. B. Wang, “Information fusion estimation based preview control for a discrete linear system,” Acta Automatica Sinica, vol. 36, no. 2, pp. 347–352, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. T. Katayama and T. Hirono, “Design of an optimal servomechanism with preview action and its dual problem,” International Journal of Control, vol. 45, no. 2, pp. 407–420, 1987. View at Publisher · View at Google Scholar · View at Scopus
  11. F. Liao, Y. Y. Tang, H. Liu, and Y. Wang, “Design of an optimal preview controller for continuous-time systems,” International Journal of Wavelets, Multiresolution and Information Processing, vol. 9, no. 4, pp. 655–673, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. F. Liao, Z. Ren, M. Tomizuka, and J. Wu, “Preview control for impulse-free continuous-time descriptor systems,” International Journal of Control, vol. 88, no. 6, pp. 1142–1149, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. F. Liao and H. Xu, “Application of the preview control method to the optimal tracking control problem for continuous-time systems with time-delay,” Mathematical Problems in Engineering, vol. 2015, Article ID 423580, 8 pages, 2015. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Åström, Introduction to Stochastic Control Theory, Translated by Yuhuan Pan, Science Press, Beijing, China, 1983. View at MathSciNet
  15. J. Wu, F. Liao, and M. Tomizuka, “Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon,” International Journal of Systems Science, vol. 48, no. 1, pp. 129–137, 2017. View at Publisher · View at Google Scholar
  16. B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, New York, NY, USA, 6th edition, 2005.
  17. T. H. Cormen, C. E. Leiserson, R. Rivest, and C. Stein, Introduction to Algorithms, MIT Press and McGraw-Hill, Boston, Mass, USA, 2nd edition, 2001. View at MathSciNet
  18. J. Yong and X. Y. Zhou, Stochastic Control: Hamiltonian Systems and HJB Equations, vol. 43, Springer, New York, NY, USA, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  19. D. Zheng, Linear System Theory, Tsinghua University Press, Beijing, China, 2002.