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Adaptive fuzzy dynamic surface control for a class of perturbed nonlinear time-varying delay systems with unknown dead-zone

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Abstract

In this paper, adaptive dynamic surface control (DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Then, by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach, the adaptive fuzzy tracking controller is designed. Our development is able to eliminate the problem of “explosion of complexity” inherent in the existing backstepping-based methods. The main advantages of our approach include: 1) for the n-th-order nonlinear systems, only one parameter needs to be adjusted online in the controller design procedure, which reduces the computation burden greatly. Moreover, the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results; 2) the proposed control scheme does not need to know the time delays and their upper bounds. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound, Finally, simulation results demonstrate the effectiveness of the proposed approach.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xidian University, Xi’an, 710071, China

    Hong-Yun Yue & Jun-Min Li

Authors
  1. Hong-Yun Yue
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  2. Jun-Min Li
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Corresponding author

Correspondence to Hong-Yun Yue.

Additional information

This work was partially supported by National Natural Science Foundation of China (Nos. 60974139 and 60804021) and Fundamental Research Funds for the Central Universities (No. 72103676).

Hong-Yun Yue graduated from Qingdao Technological University, China in 2008. She received the M. Sc. degree from Xidian University in 2011. She is currently a ph.D. candidate in Department of Applied Mathematics, Xidian University.

Her research interests include adaptive fuzzy control, neural network, robust control, and stochastic control.

Jun-Min Li graduated from Xidian University, China in 1987. He received the M. Sc. degree from Xidian University in 1990 and the Ph.D. degree from the Xi’an Jiaotong University, China in 1997. He is currently a professor in Department of Applied Mathematics, Xidian University.

His research interests include adaptive control, learning control, intelligent control, hybrid system control theory, and the networked control systems.

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Yue, HY., Li, JM. Adaptive fuzzy dynamic surface control for a class of perturbed nonlinear time-varying delay systems with unknown dead-zone. Int. J. Autom. Comput. 9, 545–554 (2012). https://doi.org/10.1007/s11633-012-0678-5

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  • DOI: https://doi.org/10.1007/s11633-012-0678-5

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