Volume 9 Number 2
April 2012
Article Contents
Qing Zhu, Ai-Guo Song, Tian-Ping Zhang and Yue-Quan Yang. Fuzzy Adaptive Control of Delayed High Order Nonlinear Systems. International Journal of Automation and Computing, vol. 9, no. 2, pp. 191-199, 2012. doi: 10.1007/s11633-012-0633-5
Cite as: Qing Zhu, Ai-Guo Song, Tian-Ping Zhang and Yue-Quan Yang. Fuzzy Adaptive Control of Delayed High Order Nonlinear Systems. International Journal of Automation and Computing, vol. 9, no. 2, pp. 191-199, 2012. doi: 10.1007/s11633-012-0633-5

Fuzzy Adaptive Control of Delayed High Order Nonlinear Systems

  • Received: 2011-06-26
Fund Project:

This work was supported by National Nature Science Foun-dation (Nos. 61174046, 61175111, 60904030, 60874045, 60874030, 60835001), University Natural Science Research Project of Jiangsu Province (No. 09KJB510019), and Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 10KJB510027).

  • This paper deals with the problem of tracking control for a class of high order nonlinear systems with input delay. The unknown continuous functions of the system are estimated by fuzzy logic systems (FLS). A state conversion method is introduced to eliminate the delayed input item. By means of the backstepping algorithm, the property of semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system is achieved. The stability of the closed-loop system is proved according to Lyapunov second theorem on stability. The tracking error is proved to be bounded which ultimately converges to an adequately small compact set. Finally, a computer simulation example of high order nonlinear systems is presented, which illustrates the effectiveness of the control scheme.
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Fuzzy Adaptive Control of Delayed High Order Nonlinear Systems

Fund Project:

This work was supported by National Nature Science Foun-dation (Nos. 61174046, 61175111, 60904030, 60874045, 60874030, 60835001), University Natural Science Research Project of Jiangsu Province (No. 09KJB510019), and Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 10KJB510027).

Abstract: This paper deals with the problem of tracking control for a class of high order nonlinear systems with input delay. The unknown continuous functions of the system are estimated by fuzzy logic systems (FLS). A state conversion method is introduced to eliminate the delayed input item. By means of the backstepping algorithm, the property of semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system is achieved. The stability of the closed-loop system is proved according to Lyapunov second theorem on stability. The tracking error is proved to be bounded which ultimately converges to an adequately small compact set. Finally, a computer simulation example of high order nonlinear systems is presented, which illustrates the effectiveness of the control scheme.

Qing Zhu, Ai-Guo Song, Tian-Ping Zhang and Yue-Quan Yang. Fuzzy Adaptive Control of Delayed High Order Nonlinear Systems. International Journal of Automation and Computing, vol. 9, no. 2, pp. 191-199, 2012. doi: 10.1007/s11633-012-0633-5
Citation: Qing Zhu, Ai-Guo Song, Tian-Ping Zhang and Yue-Quan Yang. Fuzzy Adaptive Control of Delayed High Order Nonlinear Systems. International Journal of Automation and Computing, vol. 9, no. 2, pp. 191-199, 2012. doi: 10.1007/s11633-012-0633-5
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