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Mathematical Problems in Engineering
Volume 2013, Article ID 687317, 10 pages
http://dx.doi.org/10.1155/2013/687317
Research Article

Variance and Passivity Constrained Fuzzy Control for Nonlinear Ship Steering Systems with State Multiplicative Noises

Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan

Received 7 January 2013; Accepted 18 February 2013

Academic Editor: Chang-Hua Lien

Copyright © 2013 Wen-Jer Chang and Bo-Jyun Huang. 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. P. T. K. Fung and M. J. Grimble, “Dynamic ship positioning using a self-tuning kalman filter,” IEEE Transactions on Automatic Control, vol. AC-28, no. 3, pp. 339–350, 1983. View at Google Scholar · View at Scopus
  2. J. V. Aneronger, “Adaptive steering of ships-a model reference approach,” Automatica, vol. 20, no. 1, pp. 3–14, 1984. View at Google Scholar
  3. R. E. Reid, A. K. Tugcu, and B. C. Mears, “The use of wave filter design in kalman filter state estimation of the automatic steering problem of a tanker in a seaway,” IEEE Transactions on Automatic Control, vol. AC-29, no. 7, pp. 577–584, 1984. View at Google Scholar · View at Scopus
  4. J. M. Godhavn, T. I. Fossen, and S. P. Berge, “Non-linear and adaptive backstepping designs for tracking control of ships,” International Journal of Adaptive Control and Signal Processing, vol. 12, no. 8, pp. 649–670, 1998. View at Google Scholar · View at Scopus
  5. T. I. Fossen and A. Grovlen, “Nonlinear output feedback control of dynamically positioned ships using vectorial observer backstepping,” IEEE Transactions on Control Systems Technology, vol. 6, no. 1, pp. 121–128, 1998. View at Google Scholar · View at Scopus
  6. W. J. Chang and K. Y. Chang, “Multivariable performance-constrained sliding mode control for ship Yaw-motion systems with perturbations,” International Journal of Adaptive Control and Signal Processing, vol. 14, no. 4, pp. 393–409, 2000. View at Google Scholar
  7. H. Y. Chung, S. M. Wu, and W. J. Chang, “Regional fuzzy control for nonlinear ship steering systems,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 7, pp. 1635–1646, 2008. View at Google Scholar · View at Scopus
  8. W. J. Chang, H. J. Liang, and C. C. Ku, “Fuzzy controller design subject to actuator saturation for dynamic ship positioning systems with multiplicative noises,” Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, vol. 224, no. 6, pp. 725–736, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Hotz and R. E. Skelton, “Covariance control theory,” International Journal of Control, vol. 46, no. 1, pp. 13–32, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. J. Chang and H. Y. Chung, “A study of H norm and variance-constrained design using dynamic output feedback for linear discrete systems,” International Journal of Control, vol. 57, no. 2, pp. 473–483, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W. J. Chang and J. N. Lin, “Robust dynamic controller design with multi-constraints for linear perturbed discrete systems,” Asia Journal of Control, vol. 5, no. 4, pp. 235–241, 1997. View at Google Scholar · View at Scopus
  12. Y. Hung and F. Yang, “Robust H filtering with error variance constraints for uncertain discrete time-varying systems with uncertainty,” Automatica, vol. 39, no. 7, pp. 1185–1194, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. S. Baromand and H. Khaloozadeh, “On the closed-form model for state covariance assignment problem,” IET Control Theory & Applications, vol. 4, no. 9, pp. 1678–1686, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. I. Byrnes, A. Isidori, and J. C. Willems, “Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems,” IEEE Transactions on Automatic Control, vol. 36, no. 11, pp. 1228–1240, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Xie, M. Fu, and H. Li, “Passivity analysis and passification for uncertain signal processing systems,” IEEE Transactions on Signal Processing, vol. 46, no. 9, pp. 2394–2403, 1998. View at Google Scholar · View at Scopus
  16. R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control Theory and Application, Springer, London, USA, 2000. View at MathSciNet
  17. W.-J. Chang, C. C. Ku, and W. Chang, “Analysis and synthesis of discrete nonlinear passive systems via affine T-S fuzzy models,” International Journal of Systems Science, vol. 39, no. 8, pp. 809–821, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  18. W.-J. Chang, C.-C. Ku, and P.-H. Huang, “Robust fuzzy control for uncertain stochastic time-delay Takagi-Sugeno fuzzy models for achieving passivity,” Fuzzy Sets and Systems, vol. 161, no. 15, pp. 2012–2032, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. W. J. Chang, S. S. Jheng, and C. C. Ku, “Fuzzy control with robust and passive properties for discrete-time Takagi-Sugeno fuzzy systems with multiplicative noises,” Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, vol. 226, no. 4, pp. 476–485, 2012. View at Google Scholar
  20. O. Kaneko and T. Fujii, “On discrete time nonnegative storage functions and state functions,” in Proceedings of the 39th IEEE Confernce on Decision and Control, vol. 4, pp. 3169–3174, December 2000. View at Scopus
  21. J. Mohseni, E. Yaz, and K. Olejniczak, “State-dependent LMI control of discrete-time nonlinear systems,” in Proceedings of the 37th IEEE Conference on Decision and Control (CDC '98), pp. 4626–4627, December 1998. View at Scopus
  22. S. M. Joshi, “On optimal control of linear systems in the presence of multiplicative noise,” IEEE Transactions on Aerospace and Electronic Systems, vol. AES-12, no. 1, pp. 80–85, 1976. View at Google Scholar · View at MathSciNet
  23. E. Gershon, U. Shaked, and I. Yaesh, “H control and filtering of discrete-time stochastic systems with multiplicative noise,” Automatica, vol. 37, no. 3, pp. 409–417, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. C. M. Harris and D. M. Wolpert, “Signal-dependent noise determines motor planning,” Nature, vol. 394, no. 6695, pp. 780–784, 1998. View at Publisher · View at Google Scholar · View at Scopus
  25. E. Todorov, “Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system,” Neural Computation, vol. 17, no. 5, pp. 1084–1108, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. Y. A. Phillis, “Estimation and control of systems with unknown covariance and multiplicative noise,” IEEE Transactions on Automatic Control, vol. 34, no. 10, pp. 1075–1078, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. W. J. Chang, W. Y. Wu, and C. C. Ku, “H constrained fuzzy control via state observer feedback for discrete-time Takagi-Sugeno fuzzy systems with multiplicative noises,” ISA Transactions, vol. 50, no. 1, pp. 37–43, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. W. J. Chang, L. Z. Liu, and C. C. Ku, “Passive fuzzy controller design via observer feedback for stochastic Takagi-Sugeno fuzzy models with multiplicative noises,” International Journal of Control, Automation, and Systems, vol. 9, no. 3, pp. 550–557, 2011. View at Google Scholar
  29. H. T. Yau, C. C. Wang, C. T. Hsieh, and C. C. Cho, “Nonlinear analysis and control of the uncertain micro-electro-mechanical system by using a fuzzy sliding mode control design,” Computers and Mathematics with Applications, vol. 61, no. 8, pp. 1912–1916, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. L. Huang, K. Wang, P. Shi, and H. R. Karimi, “A novel identification method for generalized T-S fuzzy systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 893807, 12 pages, 2012. View at Publisher · View at Google Scholar
  31. K. Tanaka and H.O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley & Sons, 2001.
  32. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, SIAM, Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  33. G. Eli, S. Uri, and Y. Isaac, H Control and Estimation of State-Multiplicative Linear Systems, Springer, London, UK, 2005. View at MathSciNet
  34. H. Y. Chung and W. J. Chang, “Constrained variance design for bilinear stochastic continuous systems,” IEE Proceedings D, vol. 138, no. 2, pp. 145–150, 1991. View at Google Scholar · View at Scopus