Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Sampled-data feedback and stability for a class of uncertain nonlinear systems based on characteristic modeling method

一类非线性不确定系统基于特征建模方法的采样控制及稳定性研究

Abstract

In this paper, we investigate the tracking problem for a class of second-order uncertain nonlinear systems using sampled-data output feedback. Our controller is designed based on the characteristic modeling method. We first derive the corresponding characteristic model and then give the sampled-data feedback control law, which is referred to as “golden-section adaptive control based on characteristic models”. The closed-loop system is shown to be stable and, concurrently, it is demonstrated that the tracking error can be made arbitrarily small by taking a sufficiently small sampling period. Our results improve upon the findings of previous work by removing the persistent excitation condition, and also lay certain theoretical foundations for practical applications of golden-section adaptive control.

摘要

创新点

本文研究了一类二阶非线性不确定系统的位置跟踪控制问题. 基于特征建模的思想方法,给出了一种输出采样反馈控制律—基于特征模型的黄金分割自适应控制. 证明了该控制律与原系统构成的闭环系统稳定, 并且该控制算法能够保证输出跟踪误差足够小. 该结果改进了已有研究工作中需要持续激励条件这一弊端, 为黄金分割自适应控制的工程应用提供了理论依据.

This is a preview of subscription content, log in to check access.

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 Coefficient 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 F, 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, Wuerzburg, 2013. 524–528

  9. 9

    Meng B, Wu H X. Proof of the characteristic model of the linear time invariant systems (in Chinese). Sci China Ser F-Inf Sci, 2007, 37: 1258–1271

  10. 10

    Meng B, Wu H X. On characteristic modeling of a class of flight vehicles’ attitude dynamics. Sci China Tech Sci, 2010, 53: 2074–2080

  11. 11

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

  12. 12

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

  13. 13

    Hu J. Golden-section control of the second-order plant with unknown input delay (in Chinese). Aerosp Contr Appl, 2014, 40: 1–7

  14. 14

    Huang H, Zhang Z. Characteristic model-based H2/H8 robust adaptive control during the re-entry of hypersonic cruise vehicles. Sci China Inf Sci, 2015, 58: 012202

  15. 15

    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

  16. 16

    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, in press. doi: 10.1007/s11432-015-5310-1

  17. 17

    Horn R A, Johnson C R. Matrix Analysis. New York: Combridge University Press, 1985

  18. 18

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

Download references

Author information

Correspondence to Tiantian Jiang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jiang, T., Wu, H. Sampled-data feedback and stability for a class of uncertain nonlinear systems based on characteristic modeling method. Sci. China Inf. Sci. 59, 92205 (2016). https://doi.org/10.1007/s11432-015-5496-2

Download citation

Keywords

  • uncertainty
  • nonlinear system
  • characteristic model
  • golden-section adaptive control
  • sampled-data feedback

关键词

  • 不确定性
  • 非线性系统
  • 特征模型
  • 黄金分割自适应控制
  • 采样反馈