Abstract
In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.
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This work was supported by National Natural Science Foundation of China (No. 61074014), the Outstanding Youth Funds of Liaoning Province (No. 2005219001) and Educational Department of Liaoning Province (No. 2006R29, no. 2007T80).
Chang-Liang Liu graduated with a major in mathematics education and applied mathematics from Shandong Education College, Ji’nan, PRC in 2003. He is currently working toward the M. Sc. degree in control theory and control engineering with Liaoning University of Technology, Jinzhou, PRC.
His research interests include fuzzy control theory and nonlinear adaptive control.
Shao-Cheng Tong graduated from Jinzhou Normal College, PRC in 1982. He received the M. Sc. degree from Dalian Marine University in 1988 and the Ph.D. degree from Northeastern University, PRC in 1997. He is currently a professor in the Department of Basic Mathematics, Liaoning University of Technology, PRC.
His research interests include fuzzy control theory and nonlinear adaptive control.
Yong-Ming Li graduated from Liaoning University of Technology, PRC in 2004. He received the M. Sc. degree from Liaoning University of Technology, PRC in 2007. He is currently a lecturer in the Department of Basic Mathematics, Liaoning University of Technology, PRC.
His research interests include fuzzy control theory, nonlinear adaptive control, and intelligent control.
Yuan-Qing Xia graduated from the Department of Mathematics, Chuzhou University, PRC in 1991. He received the M. Sc. degree from Anhui University, PRC in 1998 and Ph.D. degree from Beijing University of Aeronautics and Astronautics, Beijing, PRC in 2001. He is currently a professor in the Department of Automatic Control, Beijing Institute of Technology, PRC.
His research interests include networked control systems, robust control, active disturbance rejection control, and biomedical signal processing.
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Liu, CL., Tong, SC., Li, YM. et al. Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign. Int. J. Autom. Comput. 8, 14–22 (2011). https://doi.org/10.1007/s11633-010-0549-x
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DOI: https://doi.org/10.1007/s11633-010-0549-x