SCIENCE CHINA Information Sciences, Volume 59, Issue 9: 092205(2016) https://doi.org/10.1007/s11432-015-5496-2

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

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  • ReceivedJul 12, 2015
  • AcceptedOct 28, 2015
  • PublishedAug 23, 2016


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.

Funded by

National Natural Science Foundation of China(61333008)

National Key Basic Research and Development Program of China(973)




This work was supported by National Natural Science Foundation of China (Grant No. 61333008) and National Key Basic Research and Development Program of China (973) (Grant No. 2013CB733100).


[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. Google Scholar

[2] Wu H X. {All Coefficient Adaptive Control Theory and Applications (in Chinese)}. Beijing: National Defense Industry Press, 1990. Google Scholar

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

[4] Hu J. All coefficient adaptive re-entry lifting control of manned spacecraft (in Chinese). newblock J Astron, 1998, 19: 8-12 Google Scholar

[5] Hu J, Xie Y C. The all coefficient adaptive control of spacecraft instantaneous thermal current (in Chinese). newblock Contr Theor Appl, 1997, 14: 685-690 Google Scholar

[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). newblock Aerosp Contr, 2001, 19: 21-26 Google Scholar

[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). newblock Aerosp Contr Appl, 2011, 37: 1-5 Google Scholar

[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. Google Scholar

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

[10] Meng B, Wu H X. On characteristic modeling of a class of flight vehicles' attitude dynamics. newblock Sci China Tech Sci, 2010, 53: 2074-2080 CrossRef Google Scholar

[11] Xie Y C, Wu H X. The application of the golden section in adaptive robust controller design. newblock Chinese J Autom, 1992, 4: 197-205 Google Scholar

[12] Wu H X, Wang Y, Xie Y C. Nonlinear golden-section adaptive control (in Chinese). newblock J Astron, 2002, 23: 1-8 Google Scholar

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

[14] Huang H, Zhang Z. Characteristic model-based $H_2/H_\infty$ robust adaptive control during the re-entry of hypersonic cruise vehicles. newblock Sci China Inf Sci, 2015, 58: 012202-7 Google Scholar

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

[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. Google Scholar

[17] Horn R A, Johnson C R. Matrix Analysis. New York: Combridge University Press, 1985. Google Scholar

[18] Guo L. {Time-Varying Stochastic Systems--Stability, Estimation and Control (in Chinese)}. Jilin: Jilin Science and Technology Press, 1992. Google Scholar

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