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Division by zero, pseudo-division by zero, Zhang dynamics method and Zhang-gradient method about control singularity conquering

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Listed:
  • Yunong Zhang
  • Yinyan Zhang
  • Dechao Chen
  • Zhengli Xiao
  • Xiaogang Yan

Abstract

In this paper, the division-by-zero (DBO) problem in the field of nonlinear control, which is traditionally termed the control singularity problem (or specifically, controller singularity problem), is investigated by the Zhang dynamics (ZD) method and the Zhang-gradient (ZG) method. According to the impact of the DBO problem on the state variables of the controlled nonlinear system, the concepts of the pseudo-DBO problem and the true-DBO problem are proposed in this paper, which provide a new perspective for the researchers on the DBO problems as well as nonlinear control systems. Besides, the two classes of DBO problems are solved under the framework of the ZG method. Specific examples are shown and investigated in this paper to illustrate the two proposed concepts and the efficacy of the ZG method in conquering pseudo-DBO and true-DBO problems. The application of the ZG method to the tracking control of a two-wheeled mobile robot further substantiates the effectiveness of the ZG method. In addition, the ZG method is successfully applied to the tracking control of a pure-feedback nonlinear system.

Suggested Citation

  • Yunong Zhang & Yinyan Zhang & Dechao Chen & Zhengli Xiao & Xiaogang Yan, 2017. "Division by zero, pseudo-division by zero, Zhang dynamics method and Zhang-gradient method about control singularity conquering," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(1), pages 1-12, January.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:1:p:1-12
    DOI: 10.1080/00207721.2016.1139761
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    References listed on IDEAS

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    1. Editors, 2014. "International Journal of Systems Science," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 1-1, December.
    2. Ben Niu & Jun Zhao, 2013. "Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 978-985.
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