Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique

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

Volumn 41, Issue 6, 2011, Pages 1681-1692

  Wang, Min ^a   Liu, Xiaoping ^b   Shi, Peng ^c,d  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b LAKEHEAD UNIVERSITY   (Canada)

^c UNIVERSITY OF GLAMORGAN   (United Kingdom)

^d VICTORIA UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE NEURAL CONTROL; ADAPTIVE PARAMETERS; BACKSTEPPING DESIGN; CONTROL LAWS; DESIGN SCHEME; DYNAMIC SURFACE; DYNAMIC SURFACE CONTROL; HYPERBOLIC TANGENT FUNCTION; IMPLICIT FUNCTION; LYAPUNOV-KRASOVSKII FUNCTIONALS; MEAN VALUE THEOREM; NONLINEAR TERMS; NONLINEAR TIME-DELAY SYSTEMS; PURE-FEEDBACK SYSTEM; RADIAL BASIS FUNCTION NEURAL NETWORKS; RBF NEURAL NETWORK; ROBUST STABILIZATION PROBLEM; SEMI-GLOBAL; SEPARATION TECHNIQUES; SIMULATION STUDIES; UNIFORM ULTIMATE BOUNDEDNESS; VIRTUAL CONTROL;

BACKSTEPPING; DELAY CONTROL SYSTEMS; DESIGN; HYPERBOLIC FUNCTIONS; LYAPUNOV FUNCTIONS; NEURAL NETWORKS; NONLINEAR FEEDBACK; PACKAGING; RADIAL BASIS FUNCTION NETWORKS; ROBUSTNESS (CONTROL SYSTEMS); TIME DELAY;

ADAPTIVE CONTROL SYSTEMS;

EID: 81955162995     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2011.2159111     Document Type: Article

References (48)

1. M. Krsti, I. Kanellakopoulos and P. V. Kokotovi, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
2. C. Hua, X. Guan and P. Shi, "Robust backstepping control for a class of time delayed systems," IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 894-899, Jun. 2005. (Pubitemid 40902719)
3. Y. Xia, M. Fu, P. Shi, Z. Wu and J. Zhang, "Adaptive backstepping controller design for stochastic jump systems," IEEE Trans. Autom. Control, vol. 54, no. 12, pp. 2853-2859, Dec. 2009.
4. I. Kanellakopoulos, P. V. Kokotovi and R. Marino, "An extended direct scheme for robust adaptive nonlinear control," Automatica, vol. 27, no. 2, pp. 247-255, Mar. 1991.
5. M. M. Polycarpou, "Stable adaptive neural control strategy for nonlinear systems," IEEE Trans. Autom. Control, vol. 41, no. 3, pp. 447-451, Mar. 1996. (Pubitemid 126767899)
6. M.M. Polycarpou andM. J.Mears, "Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators," Int. J. Control, vol. 70, no. 3, pp. 363-384, Jun. 1998. (Pubitemid 128552923)
7. B. Chen, X. Liu and S. C. Tong, "Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 287-300, Apr. 2007. (Pubitemid 46563428)
8. M. Wang, B. Chen and S. Tong, "Adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown time delays," Int. J. Innovative Comput. Inf. Control, vol. 4, no. 4, pp. 829-838, Apr. 2008.
9. S. S. Ge, C. C. Hang, T. H. Lee and T. Zhang, Stable Adaptive Neural Network Control. Boston, MA: Kluwer, 2001.
10. C. Kwan and F. L. Lewis, "Robust backstepping control of nonlinear systems using neural networks," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 30, no. 6, pp. 753-766, Nov. 2000. (Pubitemid 32169089)
11. F. L. Lewis, A. Yesildirek and K. Liu, "Robust backstepping control of induction motors using neural networks," IEEE Trans. Neural Netw., vol. 11, no. 5, pp. 1178-1187, Sep. 2000.
12. S. C. Tong and H. X. Li, "Fuzzy adaptive sliding mode control for MIMO nonlinear systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 3, pp. 354-360, Jun. 2003.
13. Y. S. Yang, G. Feng and J. S. Ren, "A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 34, no. 3, pp. 406-420, May 2004.
14. T. Wang, S. Tong and Y. Li, "Robust adaptive fuzzy control for nonlinear system with dynamic uncertainties based on backstepping," Int. J. Innovative Comput., Inf. Control, vol. 5, no. 9, pp. 2675-2688, Sep. 2009.
15. T. Zhang, S. S. Ge and C. C. Hang, "Adaptive neural network control for strict-feedback nonlinear systems using backstepping design," Automatica, vol. 36, no. 12, pp. 1835-1846, Dec. 2000.
16. S. S. Ge and C. Wang, "Adaptive NN control of uncertain nonlinear purefeedback systems," Automatica, vol. 38, no. 4, pp. 671-682, Apr. 2002. (Pubitemid 34141010)
17. A. Ferrara and L. Giacomini, "Control of a class of mechanical systems with uncertainties via a constructive adaptive/second order VSC approach," Trans. ASME, J. Dyn. Syst. Meas. Control, vol. 122, no. 1, pp. 33-39, 2000.
18. D. Seto, A. M. Annaswamy and J. Baillieul, "Adaptive control of nonlinear systems with a triangular structure," IEEE Trans. Autom. Control, vol. 39, no. 7, pp. 1411-1428, Jul. 1994.
19. D. Wang and J. Huang, "Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form," Automatica, vol. 38, no. 8, pp. 1365-1372, Aug. 2002. (Pubitemid 34623687)
20. T. P. Zhang and S. S. Ge, "Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form," Automatica, vol. 44, no. 7, pp. 1895-1903, Jul. 2008.
21. H. Du, H. Shao and P. Yao, "Adaptive neural network control for a class of low-triangular-structured nonlinear systems," IEEE Trans. Neural Netw., vol. 17, no. 2, pp. 509-614, Mar. 2006.
22. Y. J. Liu and W. Wang, "Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems," Inf. Sci., vol. 177, no. 18, pp. 3901-3917, Sep. 2007. (Pubitemid 46961974)
23. B. Ren, S. S. Ge, C. Y. Su and T. H. Lee, "Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 39, no. 2, pp. 431-443, Apr. 2009.
24. C. Wang, D. J. Hill, S. S. Ge and G. R. Chen, "An ISS-modular approach for adaptive neural control of pure-feedback systems," Automatica, vol. 42, no. 5, pp. 723-731, May 2006.
25. S.-L. Niculescu, Delay Effects on Stability: A Robust Control Approach. New York: Springer-Verlag, 2001.
26. H. G. Zhang, Y. Wang and D. Liu, "Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 1, pp. 125-140, Feb. 2008.
27. J. Hale, Theory of Functional Differential Equations, 2nd ed. New York: Springer-Verlag, 1997.
28. M. Jankovic, "Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems," IEEE Trans. Autom. Control, vol. 46, no. 7, pp. 1048-1060, Jul. 2001. (Pubitemid 32732628)
29. X. Jiao and T. Shen, "Adaptive feedback control of nonlinear time-delay systems: The Lasalle-Razumikhin-based approach," IEEE Trans. Autom. Control, vol. 50, no. 11, pp. 1909-1913, Nov. 2005. (Pubitemid 41748899)
30. C. Hua, G. Feng and X. Guan, "Robust controller design of a class of nonlinear time delay systems via backstepping method," Automatica, vol. 44, no. 2, pp. 567-573, Feb. 2008.
31. S. S. Ge, F. Hong and T. H. Lee, "Adaptive neural network control of nonlinear systems with unknown time delays," IEEE Trans. Autom. Control, vol. 48, no. 11, pp. 2004-2010, Nov. 2003.
32. B. Chen, X. Liu, K. F. Liu and C. Lin, "Novel adaptive neural control design for nonlinear MIMO time-delay systems," Automatica, vol. 45, no. 6, pp. 1554-1560, Jun. 2009.
33. S. S. Ge, F. Hong and T. H. Lee, "Adaptive neural network control of nonlinear systems with unknown time delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 1, pp. 499-516, Feb. 2004.
34. F. Hong, S. S. Ge and T. H. Lee, "Practical adaptive neural control of nonlinear systems with unknown time delays," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 4, pp. 849-854, Aug. 2005. (Pubitemid 41644066)
35. M.Wang, B. Chen, K. Liu, X. Liu and S. Zhang, "Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients," Inf. Sci., vol. 178, no. 22, pp. 4326-4340, Nov. 2008.
36. T. P. Zhang and S. S. Ge, "Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs," Automatica, vol. 43, no. 6, pp. 1021-1033, Jun. 2007. (Pubitemid 46653816)
37. D. W. C. Ho, J. M. Li and Y. G. Niu, "Adaptive neural control for a class of nonlinearly parametric time-delay systems," IEEE Trans. Neural Netw., vol. 16, no. 3, pp. 625-635, May 2005. (Pubitemid 40718008)
38. B. Chen, X. Liu, K. Liu, P. Shi and C. Lin, "Direct adaptive fuzzy control for nonlinear systems with time-varying delays," Inf. Sci., vol. 180, no. 5, pp. 776-792, Mar. 2010.
39. M. Wang, B. Chen and P. Shi, "Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 3, pp. 721-730, Jun. 2008. (Pubitemid 351796153)
40. D. Swaroop, J. K. Hedrick, P. P. Yip and J. C. Gerdes, "Dynamic surface control for a class of nonlinear systems," IEEE Trans. Autom. Control, vol. 45, no. 10, pp. 1893-1899, Oct. 2000. (Pubitemid 32067065)
41. D. Wang and J. Huang, "Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form," IEEE Trans. Neural Netw., vol. 16, no. 1, pp. 195-202, Jan. 2005. (Pubitemid 40241920)
42. S. Tong, Y. Li and T. Wang, "Adaptive fuzzy backstepping fault-tolerant control for uncertain nonlinear systems based on dynamic surface," Int. J. Innovative Comput. Inf. Control, vol. 5, no. 10(A), pp. 3249-3261, Oct. 2009.
43. S. J. Yoo, J. B. Park and Y. H. Choi, "Adaptive dynamic surface control for stabilization of parametric strict-feedback nonlinear systems with unknown time delays," IEEE Trans. Autom. Control, vol. 52, no. 12, pp. 2360-2365, Dec. 2007.
44. S. J. Yoo, J. B. Park and Y. H. Choi, "Adaptive neural control for a class of strict-feedback nonlinear systems with state time delays," IEEE Trans. Neural Netw., vol. 20, no. 7, pp. 1209-1215, Jul. 2009.
45. R. M. Sanner and J. E. Slotine, "Gaussian networks for direct adaptive control," IEEE Trans. Neural Netw., vol. 3, no. 6, pp. 837-863, Nov. 1992.
46. T. M. Apostol, Mathematical Analysis. Reading, MA: Addison-Wesley, 1963.
47. W. Lin and C. J. Qian, "Adaptive control of nonlinearly parameterized systems: The smooth feedback case," IEEE Trans. Autom. Control, vol. 47, no. 8, pp. 1249-1266, Aug. 2002. (Pubitemid 34959759)
48. S. S. Ge and K. P. Tee, "Approximation-based control of nonlinear MIMO time-delay systems," Automatica, vol. 43, no. 1, pp. 31-43, Jan. 2007. (Pubitemid 44792031)