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.
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.
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Wu H X, Hu J, Xie Y C. Characteristic Model Based Intelligent and Adaptive Control (in Chinese). Beijing: China Science and Technology Press, 2009
Wu H X. All Coefficient Adaptive Control Theory and Applications (in Chinese). Beijing: National Defense Industry Press, 1990
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
Hu J. All coefficient adaptive re-entry lifting control of manned spacecraft (in Chinese). J Astron, 1998, 19: 8–12
Hu J, Xie Y C. The all coefficient adaptive control of spacecraft instantaneous thermal current (in Chinese). Contr Theor Appl, 1997, 14: 685–690
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
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
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
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
Meng B, Wu H X. On characteristic modeling of a class of flight vehicles’ attitude dynamics. Sci China Tech Sci, 2010, 53: 2074–2080
Xie Y C, Wu H X. The application of the golden section in adaptive robust controller design. Chinese J Autom, 1992, 4: 197–205
Wu H X, Wang Y, Xie Y C. Nonlinear golden-section adaptive control (in Chinese). J Astron, 2002, 23: 1–8
Hu J. Golden-section control of the second-order plant with unknown input delay (in Chinese). Aerosp Contr Appl, 2014, 40: 1–7
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
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
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
Horn R A, Johnson C R. Matrix Analysis. New York: Combridge University Press, 1985
Guo L. Time-Varying Stochastic Systems–Stability, Estimation and Control (in Chinese). Jilin: Jilin Science and Technology Press, 1992
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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
- nonlinear system
- characteristic model
- golden-section adaptive control
- sampled-data feedback