Kybernetika 58 no. 4, 637-660, 2022

Adaptive output feedback stabilization for nonlinear systems with unknown polynomial-of-output growth rate and sensor uncertainty

Yanjun Shen and Lei LinDOI: 10.14736/kyb-2022-4-0637

Abstract:

In this paper, the problem of adaptive output feedback stabilization is investigated for a class of nonlinear systems with sensor uncertainty in measured output and a growth rate of polynomial-of-output multiplying an unknown constant in the nonlinear terms. By developing a dual-domination approach, an adaptive observer and an output feedback controller are designed to stabilize the nonlinear system by directly utilizing the measured output with uncertainty. Besides, two types of extension are made such that the proposed methods of adaptive output feedback stabilization can be applied for nonlinear systems with a large range of sensor uncertainty. Finally, numerical simulations are provided to illustrate the correctness of the theoretical results.

Keywords:

observer, output feedback, adaptive stabilization, polynomial-of-output growth rate, measurement sensitivity

Classification:

93D15, 93D21, 93C10

paper.pdf

References:

  1. A. Benabdallah, H. Ayadi and M. Mabrouk: Adaptive regulation of uncertain nonlinear systems by output feedback: a universal control approach. Int. J. Adaptive Control Signal Process. 28 (2014), 604-619.   DOI:10.1002/acs.2412
  2. A. Benabdallah and M. Belfeki: Adaptive output feedback regulation for a class of uncertain feedforward nonlinear systems. Int. Adaptive Control Signal Process. 31 (2017), 695-709.   DOI:10.1002/acs.2703
  3. C. Chen, C. Qian, Z. Sun and Y. Liang: Global output feedback stabilization of a class of nonlinear systems with unknown measurement sensitivity. IEEE Trans. Automat. Control 63 (2018), 2212-2217.   DOI:10.1109/TAC.2017.2759274
  4. A. Chian, F. Borotto, E. Rempel and C. Rogers: Attractor merging crisis in chaotic business cycles. Chaos Solitons Fractals 24 (2005), 869-875.   DOI:10.1016/j.chaos.2004.09.080
  5. C. Guo and X. Xie: Global output feedback control of nonlinear time-delay systems with input matching uncertainty and unknown output function. Int. J. Systems Sci. 50 (2019), 713-725.   DOI:10.1080/00207721.2019.1567868
  6. Y. Huang and Y. Liu: A compact design scheme of adaptive output feedback control for uncertain nonlinear systems. Int. J. Control 92 (2017), 261-269.   DOI:10.1080/00207179.2017.1350756
  7. H. Khalil: Nonlinear Systems. Prentice Hall, Upper Saddle River, NJ 2002.   CrossRef
  8. M. Koo and H. Choi: Output feedback regulation of a class of lower triangular nonlinear systems with arbitrary unknown measurement sensitivity. Int. J. Control Automat. Systems 18 (2020), 2186-2194.   DOI:10.1007/s12555-019-0721-1
  9. P. Krishnamurthy and F. Khorrami: Generalized adaptive output feedback form with unknown parameters multiplying high output relative-degree states. IEEE Trans. Automat. Control 41 (2002), 1503-1508.   DOI:10.1109/cdc.2002.1184732
  10. M. Krstic and H. Deng: Stabilization of Uncertain Nonlinear Systems. Springer, New York 1998.   CrossRef
  11. E. Lantto: Robust Control of Magnetic Bearings in Subcritical Machines. Ph.D Dissertation, Department of Electrical Engineering, Helsinki University of Technology, Espoo 1999.   CrossRef
  12. W. Li, X. Yao and M. Krstic: Adaptive-gain observer-based stabilization of stochastic strict-feedback systems with sensor uncertainty. Automatica 120 (2020), 109112.   DOI:10.1016/j.automatica.2020.109112
  13. H. Lei and W. Lin: Universal adaptive control of nonlinear systems with unknown growth rate by output feedback. Automatica. 42 (2006), 1783-1789.   DOI:10.1016/j.automatica.2006.05.006
  14. H. Lei and W. Lin: Adaptive regulation of uncertain nonlinear systems by output feedback: a universal control approach. Systems Control Lett. 56 (2007), 529-537.   DOI:10.1016/j.sysconle.2007.03.002
  15. F. Shang, Y. Liu. and C. Zhang: Adaptive output feedback stabilization for a class of nonlinear systems with inherent nonlinearities and uncertainties. Int. J. Robust Nonlinear Control 21 (2011), 157-176.   DOI:10.1002/rnc.1583
  16. Z. Sun, J. Xing and Q. Meng: Output feedback regulation of time-delay nonlinear systems with unknown continuous output function and unknown growth rate. Nonlinear Dynamics 100 (2020), 1309-1325.   DOI:10.1007/s11071-020-05552-3
  17. D. Van: VII. Forced oscillations in a circuit with non-linear resistance. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 3 (1927), 65-80.   DOI:10.1080/14786440108564176
  18. X. Yan and Y. Liu: New results onglobal output-feedback stabilization for nonlinear systems with unknown growth rate. J. Control Theory Appl. 11 (2013), 401-408.   DOI:10.1007/s11768-013-2081-3
  19. X. Yan, Y. Liu and W. Zheng: Globally adaptive output-feedback stabilization for a class of uncertain nonlinear systems with unknown growth rate and unknown output function. Automatica 104 (2019), 173-181.   DOI:10.1016/j.automatica.2019.02.040
  20. B. Yang and W. Lin: Homogeneous observers, iterative design and global stabilization of high order nonlinear systems by smooth output feedback. IEEE Trans. Automat. Control 49 (2004), 1069-1080.   DOI:10.1109/TAC.2004.831186
  21. Y. Yu and Y. Shen: Robust sampled-data observer design for Lipschitz nonlinear systems. Kybernetika 54 (2018), 699-717.   DOI:10.14736/kyb-2018-4-0699
  22. J. Zhai, H. Du and S. Fei: Global sampled-data output feedback stabilization for a class of nonlinear systems with unknown output function. Int. J. Control 89 (2016), 469-480.   DOI:10.1080/00207179.2015.1081294
  23. J. Zhai and C. Qian: Global control of nonlinear systems with uncertain output function using homogeneous domination approach. In. J. Robust Nonlinear Control 21 (2012), 57-65.   DOI:10.1002/rnc.1765
  24. X. Zhang and W. Lin: Robust output feedback control of polynomial growth nonlinear systems with measurement uncertainty. Int. J. Robust Nonlinear Control 29 (2019), 4562-4576.   DOI:10.1002/rnc.4638
  25. D. Zhang and Y. Shen: Global output feedback sampled-date stabilization for upper-triangular nonlinear systems with improved maximum allowable transmission delay. Int. J. Robust Nonlinear Control 27 (2017), 212-235.   DOI:10.1002/rnc.3568