Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis

IEEE Transactions on Neural Networks and Learning Systems

Volumn 25, Issue 5, 2014, Pages 947-958

  Wang, Huanqing ^a,b   Chen, Bing ^a   Liu, Kefu ^c   Liu, Xiaoping ^c   Lin, Chong ^a  

^a QINGDAO UNIVERSITY   (China)

^b BOHAI UNIVERSITY   (China)

^c LAKEHEAD UNIVERSITY   (Canada)

Author keywords

Adaptive neural control; backlash like hysteresis; backstepping; nonstrict feedback structure; stochastic nonlinear systems.

Indexed keywords

APPROXIMATION ALGORITHMS; BACKSTEPPING; CLOSED LOOP CONTROL SYSTEMS; CONTROL NONLINEARITIES; FEEDBACK; HYSTERESIS;

ADAPTIVE BACKSTEPPING TECHNIQUE; ADAPTIVE NEURAL CONTROL; BACKLASH-LIKE HYSTERESIS; NON-STRICT-FEEDBACK; RADIAL BASIS FUNCTION NEURAL NETWORKS; SEMI-GLOBALLY UNIFORMLY ULTIMATELY BOUNDED; STOCHASTIC NONLINEAR SYSTEMS; UNIVERSAL APPROXIMATION;

STOCHASTIC CONTROL SYSTEMS;

BIOLOGICAL MODEL; COMPUTER SIMULATION; FEEDBACK SYSTEM; HUMAN; NERVE CELL; NONLINEAR SYSTEM; PHYSIOLOGY; STATISTICS;

COMPUTER SIMULATION; FEEDBACK; HUMANS; MODELS, NEUROLOGICAL; NEURONS; NONLINEAR DYNAMICS; STOCHASTIC PROCESSES;

EID: 84899639601     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2283879     Document Type: Article

References (48)

1. M. Krstić, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design. New York, NY, USA: Wiley, 1995.
2. I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, "Systematic design of adaptive controllers for feedback linearizable systems," IEEE Trans. Autom. Control, vol. 36, no. 11, pp. 1241-1253, Nov. 1991.
3. H. G. Zhang and L. Cai, "Decentralized nonlinear adaptive control of an HVAC system," IEEE Trans. Syst., Man Cybern. C, Appl. Rev., vol. 32, no. 4, pp. 493-498, Nov. 2002.
4. P. Florchinger, "A universal formula for the stabilization of control stochastic differential equations," Stochastic Anal. Appl., vol. 11, no. 2, pp. 155-162, Apr. 1993.
5. Z. G. Pan and T. Basar, "Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems," IEEE Trans. Autom. Control, vol. 43, no. 8, pp. 1066-1083, Aug. 1998. (Pubitemid 128737387)
6. Y. G. Liu and J. F. Zhang, "Reduced-order obserer-based control design for nonlinear stochastic systems," Syst. Control Lett., vol. 52, no. 2 pp. 123-135, Jun. 2004.
7. Y. G. Liu and J. F. Zhang, "Practical output feedback risk-sensitive control for stochastic nonlinear systems under stable zero-dynamics," SIAM J. Control Optim., vol. 45, no. 3, pp. 885-926, May 2006.
8. H. Deng and M. Krstić, "Stochastic nonlinear stabilization, Part I: A backstepping design," Syst. Control Lett., vol. 32, no. 3, pp. 143-150, Nov. 1997. (Pubitemid 127452066)
9. H. Deng and M. Krstić, "Stochastic nonlinear stabilization, Part II: Inverse optimality," Syst. Control Lett., vol. 32, no. 3, pp. 151-159, Nov. 1997. (Pubitemid 127452067)
10. H. Deng, M. Krstić, and R. J. Willians, "Stabilization of stochastic nonlinear systems driven by noise of unknown covariance," IEEE Trans. Autom. Control, vol. 46, no. 8, pp. 1237-1253, Aug. 2001. (Pubitemid 32829748)
11. H. B. Ji and H. S. Xi, "Adaptive output-feedback tracking of stochastic nonlinear systems," IEEE Trans. Autom. Control, vol. 51, no. 2, pp. 355-360, Feb. 2006.
12. S. J. Liu, J. F. Zhang, and Z. P. Jiang, "Decentralized adaptive outputfeedback stabilization for large-scale stochastic nonlinear systems," Automatica, vol. 43, no. 2, pp. 238-251, Feb. 2007.
13. X. J. Xie, N. Duan, and X. Yu, "State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamics," IEEE Trans. Autom. Control, vol. 56, no. 8, pp. 1921-1926, Aug. 2011.
14. Z. J. Wu, X. J. Xie, and S. Y. Zhang, "Adaptive backstepping controller design using stochastic small-gain theorem," Automatica, vol. 43, no. 4, pp. 608-620, Apr. 2007.
15. Y. S. Fu, Z. H. Tian, and S. J. Shi, "Output feedback stabilization for a class of stochastic time-delay nonlinear systems," IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 847-851, Jun. 2005.
16. X. J. Xie and N. Duan, "Further results on output-feedback stabilization for a class of stochastic nonlinear systems," IEEE Trans. Autom. Control, vol. 56, no. 5, pp. 1208-1213, May 2011.
17. Z. J. Wu, X. J. Xie, P. Shi, and Y. Q. Xia, "Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching," Automatica, vol. 45, no. 4, pp. 997-1004, Apr. 2009.
18. S. S. Ge, C. C. Huang, T. Lee, and T. Zhang, Stable Adaptive Neural Network Control. Norwell, MA, USA: Kluwer, 2002.
19. S. S. Ge and J. Wang, "Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients," IEEE Trans. Autom. Control, vol. 48, no. 8, pp. 1463-1469, Aug. 2003.
20. M. Chen, S. S. Ge, and B. How, "Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities," IEEE Trans. Neural Netw., vol. 21, no. 5, pp. 796-812, May 2010.
21. M. Chen, S. S. Ge, and B. B. Ren, "Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints," Automatica, vol. 47, no. 3, pp. 452-455, Mar. 2011.
22. T. Zhang, S. S. Ge, and C. C. Hang, "Stable adaptive control for a class of nonlinear systems using a modified Lyapunov function," IEEE Trans. Autom. Control, vol. 45, no. 1, pp. 129-132, Jan. 2000. (Pubitemid 30581588)
23. C. Wang, D. J. Hill, S. S. Ge, and G. Chen, "An ISS-modular approach for adaptive neural control of pure-feedback systems," Automatica, vol. 42, no. 5, pp. 723-731, May 2006.
24. C. C. Hua, X. P. Guan, and P. Shi, "Robust output feedback tracking control for time-delay systems using neural network," IEEE Trans. Neural Netw., vol. 18, no. 2, pp. 495-505, Mar. 2007. (Pubitemid 46522571)
25. C. C. Hua and X. P. Guan, "Output feedback stabilization for time-delay nonlinear inerconnected systems using neural network," IEEE Trans. Neural Netw., vol. 19, no. 4, pp. 637-688, Apr. 2008.
26. H. G. Zhang, M. Li, J. Yang, and D. D. Yang, "Fuzzy model-based robust networked control for a class of nonlinear systems," IEEE Trans. Syst., Man Cybern. A, Syst. Humans, vol. 39, no. 2, pp. 437-447, Mar. 2009.
27. B. Chen, X. P. Liu, K. F. Liu, and C. Lin, "Direct adaptive fuzzy control of nonlinear strict-feedback systems," Automatica, vol. 45, no. 6, pp. 1530-1535, Jun. 2009.
28. Y. J. Liu, W.Wang, and S. C. Tong, "Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters," IEEE Trans. Syst., Man, Cybern. A, Syst. Humans, vol. 40, no. 1, pp. 170-184, Jan. 2010.
29. T. S. Li, S. C. Tong, and G. Feng, "A novel robust adaptive fuzzy tracking control for a class of nonlinear multi-input/multi-output systems," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 150-160, Feb. 2010.
30. S. C. Tong, X. L. He, and H. G. Zhang, "A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control," IEEE Trans. Fuzzy Syst., vol. 17, no. 5, pp. 1059-1069, Oct. 2009.
31. H. E. Psillakis and A. T. Alexandridis, "NN-based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise," IEEE Trans. Neural Netw., vol. 18, no. 6, pp. 1830-1835, Nov. 2007. (Pubitemid 350148430)
32. Y. C. Wang, H. G. Zhang, and Y. Z. Wang, "Fuzzy adaptive control of stochastic nonlinear systems with unknown virtual control gain function," Acta Autom. Sinica, vol. 32, no. 2, pp. 170-178, Mar. 2006.
33. S. C. Tong, Y. Li, Y. M. Li, and Y. J. Liu, "Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 41, no. 6, pp. 1693-1704, Dec. 2011.
34. J. Li, W. S. Chen, and J. M. Li, "Adaptive NN output-feedback decentralized stabilization for a class of large-scale stochastic nonlinear strict-feedback systems," Int. J. Robust Nonlinear Control, vol. 21, no. 4, pp. 452-472, Jun. 2011.
35. W. S. Chen, L. C. Jiao, J. Li, and R. Li, "Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays," IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 40, no. 3, pp. 939-950, Jun. 2010.
36. G. Tao and P. V. Kokotovic, "Adaptive control of plants with unknown hysteresis," IEEE Trans. Autom. Control, vol. 40, no. 2, pp. 200-212, Feb. 1995.
37. X. Tan and J. S. Baras, "Modeling and control of hysteresis in magnestrictive actuators," Automatica, vol. 40, no. 9, pp. 1469-1480, Sep. 2004.
38. C. Y. Su, Y. Stepanenko, J. Svoboda, and T. P. Leung, "Robust adaptive control of a class of nonlinear systems with unknown backlashlike hysteresis," IEEE Trans. Automat. Control, vol. 45, no. 12, pp. 2427-2432, Dec. 2000. (Pubitemid 32191014)
39. C. Y. Su, M. Oya, and H. Hong, "Stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash-like hysteresis," IEEE Trans. Fuzzy Syst., vol. 11, no. 1, pp. 1-8, Feb. 2003.
40. J. Zhou, C. Y. Wen, and Y. Zhang, "Adaptive backstepping control design of a class of uncertain nonlinear systems with unknown backlash-like hysteresis," IEEE Trans. Autom. Control, vol. 49, no. 10, pp. 1751-1757, Oct. 2004.
41. B. 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.
42. 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.
43. A. J. Kurdila, F. J. Narcowich, and J. D. Ward, "Persistency of excitation in identification using radial basis function approximants," SIAM J. Control Optim., vol. 33, no. 2, pp. 625-642, 1995.
44. M. M. Ploycarpou and P. A. Ioannou, "A robust adaptive nonlinear control design," Automatica, vol. 32, no. 3, pp. 423-427, Mar. 1996. (Pubitemid 126348733)
45. R. Z. Has'minskii, Stochastic Stability of Differential Equations. Norwell, MA, USA: Kluwer, 1980.
46. F. O. Rodríguez, W. Yu, R. L. Feregrino, and J. d. J. M. Serrano, "Stable PD control for ball and beam system," in Proc. Int. Symp. Robot. Autom., Aug. 2004, pp. 333-338.
47. A. Tamasevicius, A. Namajunas, and A. Cenys, "Simple 4D chaotic oscillator," Electron. Lett., vol. 32, no. 11, pp. 957-958, May 1996. (Pubitemid 126515087)
48. S. S. Ge and C. Wang, "Uncertain chaotic system control via adaptive neural design," Int. J. Bifurcation Chaos, vol. 12, no. 5, pp. 1097-1109, 2002. (Pubitemid 34861999)