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A framework for stability analysis of high-order nonlinear systems based on the CMAC method

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Abstract

A framework for analyzing the stability of a class of high-order minimum-phase nonlinear systems of relative degree two based on the characteristic model-based adaptive control (CMAC) method is presented. In particular, concerning the tracking problem for such high-order nonlinear systems, by introducing a consistency condition for quantitatively describing modeling errors corresponding to a group of characteristic models together with a certain kind of CMAC laws, we prove closed-loop stability and show that such controllers can make output tracking error arbitrarily small. Furthermore, following this framework, with a specific characteristic model and a golden-section adaptive controller, detailed sufficient conditions to stabilize such groups of highorder nonlinear systems are presented and, at the same time, tracking performance is analyzed. Our results provide a new perspective for exploring the stability of some high-order nonlinear plants under CMAC, and lay certain theoretical foundations for practical applications of the CMAC method.

抽象

创新点

本文建立了基于特征模型的采样控制方法与一类高阶对象组成闭环系统的稳定性分析框架. 具体针对一类相对阶为二的 最小相位非线性不确定系统的位置跟踪问题, 通过引入刻画特征模型容许建模误差的相容性条件, 证明了一类基于特征 模型的采样控制器与原系统组成闭环系统的稳定性, 并且输出跟踪误差能够保证足够小. 进一步根据所建立的稳定性分 析框架, 针对上述位置跟踪问题, 给出了对应的特征模型, 黄金分割自适应控制, 以及具体的闭环稳定条件. 本文的研 究结果为基于特征模型自适应控制方法的闭环稳定性分析提供了新的研究思路, 为该方法的工程应用奠定了理论基础.

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References

  1. 1

    Wu H X, Hu J, Xie Y C. Characteristic Model Based Intelligent and Adaptive Control (in Chinese). Beijing: China Science and Technology Press, 2009

  2. 2

    Wu H X. All Coeffieicent Adaptive Control Theory and Applications (in Chinese). Beijing: National Defense Industry Press, 1990

  3. 3

    Wu H X, Hu J, Xie Y C. Characteristic model-based all-coefficient adaptive control method and its applications. IEEE Trans Syst Man Cybern Part C-Appl Rev, 2007, 37: 213–221

  4. 4

    Hu J. All coefficient adaptive re-entry lifting control of manned spacecraft (in Chinese). J Astron, 1998, 19: 8–12

  5. 5

    Hu J, Xie Y C. The all coefficient adaptive control of spacecraft instantaneous thermal current (in Chinese). Contr Theor Appl, 1997, 14: 685–690

  6. 6

    Wang Y C, Geng C G, Wu H X. An adaptive fuzzy controller and its application in the process control of aluminum electrolysis (in Chinese). Aerosp Contr, 2001, 19: 21–26

  7. 7

    Hu J, Xie Y C, Zhang H, et al. Shenzhou-8 spacecraft guidance, navigation and control system and flight result evaluation for rendezvous and docking (in Chinese). Aerosp Contr Appl, 2011, 37: 1–5

  8. 8

    Xie Y C, Hu J, Wang M, et al. Accurate and stable control of Shenzhou spacecraft in rendezvous and docking. In: Proceedings of the 19th IFAC Symposium on Automatic Control in Aerospace, Germany, 2013. 524–528

  9. 9

    Xie Y C, Wu H X. The application of the golden section in adaptive robust controller design. Chinese J Autom, 1992, 4: 197–205

  10. 10

    Wu H X, Wang Y, Xie Y C. Nonlinear golden-section adaptive control (in Chinese). J Astron, 2002, 23: 1–8

  11. 11

    Qi C Z. Study on TDRS multi-variable adaptive control method (in Chinese). Dissertation for Ph.D. Degree. Beijing: Beijing Institute of Control Engineering, 1999

  12. 12

    Zhang Z, Hu J. Stability analysis of a hypersonic vehicle controlled by the characteristic model based adaptive controller. Sci China Inf Sci, 2012, 55: 2243–2256

  13. 13

    Wang L J. On distributed output feedback consensus of multiple robotic manipulators (in Chinese). Dissertation for Ph.D. Degree. Beijing: Beijing Institute of Control Engineering, 2015

  14. 14

    Huang J F, Kang Y, Meng B, et al. Characteristic model based adaptive controller design and analysis for a class of SISO systems. Sci China Inf Sci, 2015, 59: 052202

  15. 15

    Nešić D, Teel A R, Kokotović P V. Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations. Syst Contr Lett, 1999, 38: 259–270

  16. 16

    Nešić D, Teel A R. A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. IEEE Trans Automat Contr, 2004, 49: 1103–1122

  17. 17

    Wang Y. Stability analysis of characteristic model based all-coefficient adaptive method for a class of minimum-phase nonlinear systems (in Chinese). Contr Theor Appl, 2012, 29: 1097–1107

  18. 18

    Jiang T T, Wu H X. Sampled-data feedback and stability for a class of uncertain nonlinear systems based on characteristic modeling method. Sci China Inf Sci, 2016, 59: 092205

  19. 19

    Wu H X, Liu Y W, Liu Z H, et al. Characteristic modeling and flexible structure control (in Chinese). Sci China Ser E-Tech Sci, 2001, 31: 137–149

  20. 20

    Chen L, Yan Y, Sun C Y. Nonlinear characteristic model based SMC and its application to flexible satellites. In: Proccedings of the 19th World Congress the International Federation of Automatic Control, Cape Town, 2014. 4595–4600

  21. 21

    Khalil H K. Nonlinear Systems. 3rd ed. Englewood Cliffs: Prentice Hall, 2002

  22. 22

    Horn R A, Johnson C R. Matrix Analysis. New York: Cambridge Univ Press, 1985

  23. 23

    Isidori A. Nonlinear Control Systems. 3rd ed. London: Springer-Verlag, 1995

  24. 24

    Sun J G. Matrix Perturbation Analysis. 2nd ed. Beijing: Science Press, 2001

  25. 25

    Guo L. Time-Varying Stochastic Systems–Stability, Estimation and Control (in Chinese). Jilin: Jilin Science and Technology Press, 1992

  26. 26

    Yu X X, Xie Y C. The attitude control of assembled spacecraft by using intelligent adaptive control method (in Chinese). Aerop Contr Appl, 2009, 35: 36–41

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Correspondence to Tiantian Jiang.

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Jiang, T., Wu, H. A framework for stability analysis of high-order nonlinear systems based on the CMAC method. Sci. China Inf. Sci. 59, 112201 (2016). https://doi.org/10.1007/s11432-016-5568-y

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Keywords

  • characteristic model
  • characteristic model-based adaptive control (CMAC)
  • consistency condition
  • stability
  • high-order nonlinear system

关键词

  • 特征模型
  • 黄金分割自适应控制
  • 相容性条件
  • 稳定性
  • 高阶非线性系统