A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans.

Volumn 34, Issue 3, 2004, Pages 406-420

  Yang, Yansheng ^a   Feng, Gang ^b   Ren, Junsheng ^a  

^a Navigation Coll of Maritime Univ   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Backstepping technique; Fuzzy control; Robust adaptive control; Robust adaptive sliding control; Small gain approach; Uncertain nonlinear systems

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; ALGORITHMS; APPROXIMATION THEORY; FEEDBACK CONTROL; FUZZY CONTROL; FUZZY SETS; ROBUSTNESS (CONTROL SYSTEMS); SLIDING MODE CONTROL; UNCERTAIN SYSTEMS;

BACKSTEPPING TECHNIQUE; SMALL GAIN APPROACH;

NONLINEAR CONTROL SYSTEMS;

EID: 2442482637     PISSN: 10834427     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCA.2004.824870     Document Type: Article

References (55)

1. A. Isidori, Nonlinear Control Systems. Berlin, Germany: Springer-Verlag, 1989.
2. S. S. Sastry and A. Isidori, "Adaptive control of linearization systems," IEEE Trans. Automat. Contr., vol. 34, pp. 1123-1131, Nov. 1989.
3. D. G. Taylor, P. V. Kokotovic, R. Marino, and I. Kaellakopoulos, "Adaptive regulation of nonlinear systems with unmodeled dynamics," IEEE Trans. Automat. Contr., vol. 34, pp. 405-421, Apr. 1989.
4. I. Kanellakopoulos, P. V. Kokotovic, and R. Marino, "Robustness of adaptive nonlinear control under an extended matching condition," in Proc. IFAC Symp. Nonlinear Control Systems Design, Capri, Italy, pp. 192-197.
5. J. B. Pomet and L. Praly, "Adaptive nonlinear regulation: Estimation from the Lyapunov equation," IEEE Trans. Automat. Contr., vol. 37, pp. 729-740, June 1992.
6. M. J. Corless and G. Leitmann, "Continuus state feedback guranteeing uniform ultimate boundedness for uncertain dynamic systems," IEEE Trans. Automat. Contr., vol. AC-26, pp. 1139-1144, 1981.
7. B. R. Barmish and G. Leitmann, "On ultimate boundedness control of uncertain systems in the absence of matching assumptions," IEEE Trans. Automat. Contr., vol. AC-27, pp. 153-158, Feb. 1982.
8. V. I. Utkin, Sliding Modes in Control Optimization. New York: Springer-Verlag, 1992.
9. A. S. I. Zinober, Deterministic Control of Uncertain Control System. London, U.K.: Peregrinus, Stevenage, 1990.
10. M. M. Polycarpou and P. A. Ioannou, "Identification and Control using Neural Network Models: Design and Stability Analysis," Univ. Southern California, Dept. Elect. Eng. Syst., Los Angeles, Tech. Rep. 91-09-01 1991.
11. S. S. Sanner and J. E. Slotine, "Gaussian networks for direct adaptive control," IEEE Neural Networks, vol. 3, pp. 837-863, Nov. 1992.
12. F. C. Chen and C. C. Liu, "Adaptive controlling nonlinear continuous-time systems using multilayer neural networks," Automat. Contr., vol. 39, pp. 1306-1310, 1994.
13. A. Yesidirek and F. L. Lewis, "Feedback linearization using neural networks," Automatica, vol. 31, pp. 1659-1664, 1995.
14. S. Fabri and V. Kadirkamanathan, "Dynamic structure neural networks for stable adaptive control of nonlinear systems," IEEE Trans. Neural Networks, vol. 7, pp. 1151-1167, Sept. 1996.
15. S. Jagannathan, S. Commuri, and F. L. Lewis, "Feedback linearization using CMAC neural networks," Automatica, vol. 34, no. 5, pp. 547-557, 1998.
16. S. S. Ge, T. H. Lee, and C. J. Harris, Adaptive Neural Network Control of Robotic Manipulators. Singapore: World Scientific, 1998.
17. L. X. Wang, "Fuzzy systems are universal approximators," in Proc. IEEE. Int. Conf. Fuzzy Systems, San Diego, CA, 1992, pp. 1163-1170.
18. L. X. Wang and J. M. Mendel, "Fuzzy basis functions universal approximation, and orthogonal least-squares learning," IEEE Trans. Neural Networks, vol. 3, pp. 807-814, Sept. 1992.
19. L. X. Wang, "Stable adaptive fuzzy control of nonlinear systems," IEEE Trans. Fuzzy Syst., vol. 1, pp. 146-155, May 1993.
20. C. Y. Su and Y. Stepanenko, "Adaptive control of a class of nonlinear systems with fuzzy logic," IEEE Trans. Fuzzy Syst., vol. 2, pp. 285-294, Nov. 1994.
21. Y. S. Yang, X. L. Jia, and C. J. Zhou, "Robust adaptive fuzzy control for a class of uncertain nonlinear systems," in Proc. 4th Int. Conf. Intelligent Techniques Soft Computing Nuclear Science Engineering, Brugge, Belgium, 2000.
22. J. T. Spooner and K. M. Passino, "Stable adaptive control using fuzzy systems and neural networks," IEEE Trans. Fuzzy Syst., vol. 4, pp. 339-359, Aug. 1996.
23. K. Fischle and D. Schroder, "An improved stable adaptive fuzzy control method," IEEE Trans. Fuzzy Syst., vol. 7, pp. 27-40, Feb. 1999.
24. Y. S. Yang and J. S. Ren, "Adaptive fuzzy robust tracking controller design via small gain approach and its application," IEEE Trans. Fuzzy Syst., vol. 11, pp. 1-13, Dec. 2003.
25. ∞ tracking design of uncertain nonlinear SISO systems: Adaptive fuzzy approach," IEEE Trans. Fuzzy Syst., vol. 4, pp. 32-43, Feb. 1996.
26. ∞ approaches," IEEE Trans. Fuzzy Syst., vol. 9, pp. 278-292, Apr. 2001.
27. I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, "Systematic design of adaptive controllers for feedback linearizable systems," IEEE Trans. Automat. Contr., vol. 36, pp. 1241-1253, Nov. 1991.
28. R. Marino and P. Tomei, "Global adaptive output-feedback control of nonlinear systems, Part I: Linear parameterization - Part II: Nonlinear parameterization," IEEE Trans. Automat. Contr., vol. 38, pp. 33-49, Jan. 1993.
29. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
30. M. M. Polycarpou and P. A. Ioannou, "A robust adaptive nonlinear control design," Automatica, vol. 32, pp. 423-427, 1996.
31. B. Yao and M. Tomizuka, "Adaptive robust control of SISO nonlinear systems in a semi-strict feedfack form," Automatica, vol. 33, pp. 893-900, 1997.
32. M. M. Polycarpou and J. M. Mark, "Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators," Int. J. Contr., vol. 70, pp. 363-384, 1998.
33. ∞ tracking performance," IEEE Trans. Syst., Man, Cybern. B, vol. 30, pp. 878-885, Dec. 2000.
34. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man., Cybern., vol. SMC-15, pp. 116-132, 1985.
35. E. D. Sontag, "Smooth stabilization implies coprime factorization," Automat. Contr., vol. 34, pp. 1411-1428, 1989.
36. Z. P. Jiang, A. Teel, and L. Praly, "Small-gain theorem for ISS systems and applications," Math. Contr., Sig. Syst., vol. 7, pp. 95-120, 1994.
37. L. X. Wang, A Course in Fuzzy Systems and Control. Englewood Cliffs, NJ: Prentice-Hall, 1997.
38. E. D. Sontag, "Further results about input-state stabilization," Automat. Contr., vol. 35, pp. 473-476, 1990.
39. E. D. Sontag and Y. Wang, "On characterization of input-to-state stability property with respect to compact sets," in Proc. Prep. IFAC NOLCOS, Tahoe City, 1995, pp. 226-231.
40. E. D. Sontag, "On the input-to-state stability property," vol. 1, pp. 24-36, 1995.
41. Z. P. Jiang and L. Praly, "Technical results for the study of robustness of Lagrange stability," Syst. Contr. Lett., vol. 23, pp. 67-78, 1994.
42. J. Tsinias, "Sontag's 'input-to-state stability condition' and global stabilization using state detection," Syst. Contr. Lett., vol. 20, pp. 219-226, 1993.
43. L. Praly and Z. P. Jiang, "Stabilization by output feedback for systems with ISS inverse dynamics," Syst. Contr. Lett., vol. 21, pp. 19-33, 1993.
44. L. Praly and Y. Wang, "Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability," Math., Contr., Sig. Syst., vol. 9, pp. 1-33, 1996.
45. Z. P. Jiang and I. Mareels, "A small gain control method for nonlinear cascaded systems with dynamic uncertainties," Automat. Contr., AC-42, pp. 292-308, 1997.
46. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1996.
47. M. Rios-Bolivar and A. S. I. Zinober, "Dynamical adaptive sliding mode output tracking control of a class nonlinear systems," Int. J. Robust Nonlinear Contr., vol. 7, pp. 387-405, 1997.
48. M. Rios-Bolivar, A. S. I. Zinober, and H. Sira-Ramirez, "Dynamical sliding mode control via adaptive input-output linearization: A backstepping approach," in Robust Control via Variable Structure and Lyapunov Techniques, F. Garofalo and L. Glielmo, Eds. New York: Springer-Verlag, pp. 15-35.
49. A. J. Koshkouei and A. S. I. Zinober, "Adaptive sliding backstepping control of nonlinear semi-strict feedback form systems," in Proc. IEEE 7th Mediterranean Control Conf., Haifa, Israel, 1999.
50. ____, "Adaptive output tracking backstepping sliding mode control of nonlinear systems," in Proc. 5th IFAC Symposium Robust Control Design, Prague, Czech. Republic, 2000.
51. M. Rios-Bolivar and A. S. I. Zinober, "A symbolic computation toolbox for the design of dynamical adaptive nonlinear control," Appl. Math. Comput. Sci., vol. 8, pp. 78-88, 1998.
52. T. Zhang, S. S. Ge, and C. C. Hang, "Stable adaptive control for a class on nonlinear systems using a modified Lyapunov function," IEEE Trans. Automat. Contr., vol. 45, pp. 129-132, Jan. 2000.
53. S. Gutman, "Uncertain dynamical system-A Lyapunov min max approach," IEEE Trans. Automat. Contr., vol. AC-24, pp. 437-443, June 1979.
54. C. M. Kwan, "Sliding mode control of linear systems with mismatched uncertainties," Automatica, vol. 31, pp. 303-307, 1995.
55. M. W. Spong and M. Vidyasagar, Robot Dynamics and Control. New York: Wiley.