Robust H∞ fuzzy control for a class of uncertain discrete fuzzy bilinear systems

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 38, Issue 2, 2008, Pages 510-527

  Li, Tzuu Hseng S ^a   Tsai, Shun Hung ^a   Lee, Jia Zhen ^a   Hsiao, Ming Ying ^a,b   Chao, Chan Hong ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b FORTUNE INSTITUTE OF TECHNOLOGY   (Taiwan)

Author keywords

Discrete fuzzy bilinear system (DFBS); Linearmatrix inequality (LMI); Parallel distributed compensation (PDC); Robust H control; Takagi Sugeno (T S) fuzzy model; Van de Vusse example

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP SYSTEMS; COMPUTER SIMULATION; DISCRETE TIME CONTROL SYSTEMS; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; UNCERTAIN SYSTEMS;

DISCRETE FUZZY BILINEAR SYSTEM; PARALLEL DISTRIBUTED COMPENSATION METHOD; TAKAGI-SUGENO FUZZY MODEL;

OPTIMAL CONTROL SYSTEMS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; FEEDBACK SYSTEM; FUZZY LOGIC; INFORMATION RETRIEVAL; METHODOLOGY; SIGNAL PROCESSING; STATISTICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; FEEDBACK; FUZZY LOGIC; INFORMATION STORAGE AND RETRIEVAL; LINEAR MODELS; PATTERN RECOGNITION, AUTOMATED; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 41649102861     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2007.914706     Document Type: Article

References (53)

1. R. R. Mohler, Nonlinear Systems, vol. 2. Englewood Cliffs, NJ: Prentice-Hall, 1991.
2. R. R. Mohler, Bilinear Control Processes. New York: Academic, 1973.
3. G. Y. Tang, H. Ma, and B. L. Zhang, "Successive-approximation approach of optimal control for bilinear discrete-time systems," Proc. Inst. Electr. Eng. - Control Theory Appl., vol. 152, no. 6, pp. 639-644, Nov. 2005.
4. Y. Cheng, "Controllability of switched bilinear systems," IEEE Trans. Autom. Control, vol. 50, no. 4, pp. 511-515, Apr. 2005.
5. Y.-J. Sun, "Limit cycles design for a class of bilinear control systems," Chaos, Solitons Fractals, vol. 33, no. 1, pp. 156-162, Jul. 2007.
6. ∞ reduced order filtering for uncertain bilinear systems," Automatica, vol. 42, no. 3, pp. 405-415, Mar. 2006.
7. C. W. Wang, W.-Y. Wang, and M. L. Chan, "Design of sliding mode controllers for bilinear systems with time varying uncertainties," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 1, pp. 639-645, Jul. 2004.
8. S. Gibson, A. Wills, and B. Ninness, "Maximum-likelihood parameter estimation of bilinear systems," IEEE Trans. Autom. Control, vol. 50, no. 10, pp. 1581-1596, Oct. 2005.
9. J.-S. Chiou, F.-C. Kung, and T.-H. S. Li, "Robust stabilization of a class of singularly perturbed discrete bilinear systems," IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1187-1190, Jun. 2000.
10. E. Zerrik, M. Ouzahra, and K. Ztot, "Regional stabilisation for infinite bilinear systems," Proc. Inst. Electr. Eng. - Control Theory Appl., vol. 151, no. 17, pp. 109-116, Jan. 2004.
11. Y.-J. Kim, B.-S. Kim, and M.-T. Lim, "Composite control for singularity perturbed bilinear systems via successive Galerkin approximation," Proc. Inst. Electr. Eng. - Control Theory Appl., vol. 150, no. 5, pp. 483-488, 2003.
12. C. W. Tao and J. S. Taur, "Robust fuzzy control for a plant with fuzzy linear model," IEEE Trans. Fuzzy Syst., vol. 13, no. 1, pp. 30-41, Feb. 2005.
13. C.-S. Tseng, B.-S. Chen, and H.-J. Uang, "On maximum stability margin design of nonlinear uncertain systems: Fuzzy control approach," Asian J. Control, vol. 3, no. 3, pp. 190-203, 2001.
14. K. Kiriakidis, "Fuzzy model-based control of complex plants," IEEE Trans. Fuzzy Syst., vol. 6, no. 4, pp. 517-529, Nov. 1998.
15. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no. 1, pp. 116-132, May 1985.
16. S.-H. Tsai and T.-H. S. Li, "Robust fuzzy control of a class of fuzzy bilinear systems with time-delay," Chaos, Solitons & Fractals, to be published. [Online]. Available: DOI: 10.1016/j.chaos.2007.06.057
17. C.-L. Chen, G. Feng, and G. X.-P. Guan, "Delay-dependent stability analysis and controller synthesis for discrete-time T-S fuzzy systems with time delays," IEEE Trans. Fuzzy Syst., vol. 13, no. 5, pp. 630-643, Oct. 2005.
18. G. Feng, "A survey on analysis and design of model-based fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 14, no. 5, pp. 676-697, Oct. 2006.
19. T.-H. S. Li and K.-J. Lin, "Stabilization of singularly perturbed fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 12, no. 5, pp. 579-595, Oct. 2004.
20. ∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers," IEEE Trans. Fuzzy Syst., vol. 13, no. 1, pp. 82-93, Feb. 2005.
21. Y.-C. Chen, "Intelligent robust control for uncertain nonlinear time-varying systems and its application to robotic systems," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1108-1119, Dec. 2005.
22. T.-H. S. Li and S.-J. Chang, "Autonomous fuzzy parking control of a car-like mobile robot," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 55, no. 4, pp. 451-465, Jul. 2003.
23. T.-H. S. Li, S.-J. Chang, and W. Tong, "Fuzzy target tracking control of autonomous mobile robots by using infrared sensors," IEEE Trans. Fuzzy Syst., vol. 12, no. 4, pp. 491-501, Aug. 2004.
24. H. K. Lam and F. H. F. Leung, "Stability analysis of fuzzy control systems subject to uncertain grades of membership," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1322-1325, Dec. 2005.
25. J.-H. Li, T.-H. S. Li, and T.-H. Ou, "Design and implementation of fuzzy sliding-mode controller for a wedge balancing system," J. Intell. Robot. Syst., vol. 37, no. 3, pp. 285-306, Jul. 2003.
26. H. J. Lee, J. B. Park, and G. Chen, "Robust fuzzy control of nonlinear systems with parametric uncertainties," IEEE Trans. Fuzzy Syst., vol. 9, no. 2, pp. 369-379, Apr. 2001.
27. B. S. Chen, C. S. Tseng, and H. J. Uang, "Robustness design of nonlinear dynamic systems via fuzzy linear control," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 571-585, Oct. 1999.
28. M. Margaliot and G. Langholz, "A new approach to fuzzy modeling and control of discrete-time systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 4, pp. 486-494, Aug. 2003.
29. H. K. Lam, F. H. F. Leung, and P. K. S. Tam, "Stable and robust fuzzy control for uncertain nonlinear systems," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 30, no. 6, pp. 825-840, Nov. 2000.
30. D. Huang and S. K. Nguang, "Robust H∞ static output feedback control of fuzzy systems: An ILMI approach," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 36, no. 1, pp. 216-222, Feb. 2006.
31. H. O. Wang, K. Tanaka, and M. F. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, Feb. 1996.
32. K. Tanaka, T. Ikeda, and H. O. Wang, "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability H∞ control theory, and linear matrix inequalities," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 1-13, Feb. 1996.
33. F. H. Hsiao, C.-W. Chen, Y.-W. Liang, S.-D. Xu, and W.-L. Chiang, "T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays," IEEE Trans. Fuzzy Syst., vol. 52, no. 9, pp. 1883-1893, Sep. 2005.
34. K. R. Lee, J. H. Kim, E. T. Jeung, and H. B. Park, "Output feedback H∞ robust control of uncertain fuzzy dynamic systems with time-varying delay," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 657-664, Dec. 2000.
35. Y.-C. Chang, "Intelligent robust control for uncertain nonlinear time-varying systems and its application to robotic systems," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1108-1119, Dec. 2005.
36. S. F. Su, Z. J. Lee, and Y.-P. Wang, "Robust and fast learning for fuzzy cerebellar model articulation controllers," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 36, no. 1, pp. 203-208, Feb. 2006.
37. J.-C. Lo and M.-L. Lin, "Robust H∞ control for fuzzy systems with Frobenius norm-bounded uncertainties," IEEE Trans. Fuzzy Syst. vol. 14, no. 1, pp. 1-15, Feb. 2006.
38. H.-X. Li, L. Zhang, K.-Y. Cai, and G. Chen, "An improved robust fuzzy-PID controller with optimal fuzzy reasoning," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1283-1294, Dec. 2005.
39. K. Tanaka and M. Sano, "A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer," IEEE Trans. Fuzzy Syst., vol. 2, no. 2, pp. 119-134, May 1994.
40. X. Jiang and Q. L. Sano, "Robust H∞ control for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 321-331, Apr. 2007.
41. S.-S. Chen, Y.-C. Chang, S.-F. Su, S.-L. Chung, and T.-T. Lee, "Robust static output-feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach," IEEE Trans. Fuzzy Syst. vol. 13, no. 2, pp. 263-272, Apr. 2005.
42. F. H. Hsiao, J. D. Hwang, C.-W. Chen, and Z.-R. Tsai, "Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control," IEEE Trans. Fuzzy Syst., vol. 13, no. 1, pp. 152-163, Feb. 2005.
43. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001.
44. Y. M. Zhang, E. Liguo, and B. Walcott, "Robust control of pulsed gas metal arc welding," Trans. ASME, J. Dyn. Syst. Meas. Control, vol. 124, no. 2, pp. 281-289, Jun. 2002.
45. C. Abdallah, P. Dorato, F. Pérez, and D. Docampo, "Controller synthesis for a class of interval plants," Automatica, vol. 31, no. 2, pp. 341-343, Feb. 1995.
46. H. Perez, B. Ogunnaike, and S. Devasia, "Output tracking between operating points for nonlinear processes: Van de Vusse example," IEEE Trans. Control Syst. Technol., vol. 10, no. 4, pp. 611-617, Jul. 2002.
47. C. Kravaris, M. Niemiec, R. Berber, and C. B. Brosilow, "Nonlinear model-based control of nonminimum-phase processes," in Nonlinear Model Based Process Control, ser. NATO ASI Series, vol. 353, R. Berber and C. Kravaris, Eds. Norwell, MA: Kluwer, 1998, pp. 115-142.
48. F. J. Doyle, B. A. Ogunnaike, and R. K. Pearson, "Nonlinear model-based control using second-order Volterra models," Automatica, vol. 31, no. 5, pp. 697-714, May 1995.
49. C. Kravaris and P. Daoutidis, "Nonlinear state feedback control of second-order nonminimum phase nonlinear systems," Comput. Chem. Eng. vol. 14, no. 4/5, pp. 439-449, 1990.
50. F. Doyle, F. Allgöwer, E. Gilles, and M. Morari, "On nonlinear systems with poorly behaved zero dynamics," in Proc. ACC, Chicago, IL, Jun. 1992, vol. 4, pp. 2571-2575.
51. T.-H. S. Li and S.-H. Tsai, "T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems," IEEE Trans. Fuzzy Syst., vol. 15, no. 3, pp. 494-506, Jun. 2007.
52. L. Wang, W. Liu, H. Shi, and J.M. Zurada, "Cellular neural networks with transient chaos," IEEE Trans. Circuits Syst. II, Exp. Briefs vol. 54, no. 5, pp. 440-444, May 2007.
53. S. Pederson and M. Sambandham,, "Numerical solution to hybrid fuzzy systems," Math. Comput. Model., vol. 45, no. 5, pp. 1133-1144, 2007.