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Adaptive Neural Control for Output-Constrained Pure-Feedback Systems

출력 제약된 Pure-Feedback 시스템의 적응 신경망 제어

  • Kim, Bong Su (School of Electrical and Electronics Engineering, Chung-Ang University) ;
  • Yoo, Sung Jin (School of Electrical and Electronics Engineering, Chung-Ang University)
  • 김봉수 (중앙대학교 전자전기공학부) ;
  • 유성진 (중앙대학교 전자전기공학부)
  • Received : 2013.10.09
  • Accepted : 2013.11.18
  • Published : 2014.01.01

Abstract

This paper investigates an adaptive approximation design problem for the tracking control of output-constrained non-affine pure-feedback systems. To satisfy the desired performance without constraint violation, we employ a barrier Lyapunov function which grows to infinity whenever its argument approaches some limits. The main difficulty in dealing with pure-feedback systems considering output constraints is that the system has a non-affine appearance of the constrained variable to be used as a virtual control. To overcome this difficulty, the implicit function theorem and mean value theorem are exploited to assert the existence of the desired virtual and actual controls. The function approximation technique based on adaptive neural networks is used to estimate the desired control inputs. It is shown that all signals in the closed-loop system are uniformly ultimately bounded.

Keywords

References

  1. K. P. Tee, S. S. Ge, and E. H. Tay, "Barrier Lyapunov Functions for the control of output-constrained nonlinear systems," Automatica, vol. 45, no. 4, pp. 918-927, Apr. 2009. https://doi.org/10.1016/j.automatica.2008.11.017
  2. K. P. Tee and S. S. Gee, "Control of nonlinear systems with full state constraint using a barrier Lyapunov function," in Proc. of the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, pp. 8618-8623, Dec. 2009.
  3. K. P. Tee and S. S. Gee, "Control of nonlinear systems with partial state constraints using a barrier Lyapunov function," International Journal of Control, vol. 84, no. 12, pp. 2008-2023, Dec. 2011. https://doi.org/10.1080/00207179.2011.631192
  4. Y. M. Li, T. S. Li, and X. J. Jing, "Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function," International Journal of Adaptive Control and Signal Processing, DOI: 10.1002/acs.2410, 2013.
  5. B. Niu and J. Zhao, "Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function," International Journal of Systems Science, vol. 44, no. 5, pp. 978-985, May 2013. https://doi.org/10.1080/00207721.2011.652222
  6. S. S. Ge and C. Wang, "Adaptive NN control of uncertain nonlinear pure-feedback systems," Automatica, vol. 38, pp. 671-682, 2002. https://doi.org/10.1016/S0005-1098(01)00254-0
  7. D. Wang and J. Huang, "Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form," Automatica, vol. 38, pp. 1365-1372, Jan. 2002. https://doi.org/10.1016/S0005-1098(02)00034-1
  8. C. Wang, D. J. Hill, S. S. Gee, and G. Chen, "An ISS-modular approach for adaptive neural control of pure-feedback systems," Automatica, vol. 42, pp. 723-731, May 2006. https://doi.org/10.1016/j.automatica.2006.01.004
  9. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, Hoboken, NJ: Wiley, 1995.
  10. J. H. Shin, "Robust adaptive fuzzy backstepping control for trajectory tracking of an electrically driven nonholonomic mobile robot with uncertainties" Journal of Institute of Control, Robotics and Systems (in Korean), vol. 18, no. 10, pp. 902-911, 2012. https://doi.org/10.5302/J.ICROS.2012.18.10.902
  11. J. Y. Choi, "Exponential stability of predictor feedback for discrete-time linear systems with input delays," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 19, no. 7, pp. 583-586, 2013. https://doi.org/10.5302/J.ICROS.2013.13.1913