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Stability analysis of golden-section adaptive control systems based on the characteristic model

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Abstract

All-coefficient adaptive control theory and method based on characteristic models have already been applied successfully in the fields of astronautics and industry. However, the stability analysis of the characteristic model-based golden-section adaptive control systems is still an open question in both theory and practice. To investigate such stability issues, the author first provides a method for choosing initial parameter values and new performances for a projection algorithm with dead zone for adaptive parameter estimation, and develops some properties of time-varying matrices by utilizing some algebraic techniques. And then a new Lyapunov function with logarithmic form for time-varying discrete systems is constructed. Finally, the author transforms the characteristic models of some multi-input and multi-output (MIMO) controlled systems into their equivalent form, and proves the stability of the closed-loop systems formed by the golden-section adaptive control law based on the characteristic model using mathematical techniques.

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Acknowledgments

This work was supported by National Nature Science Foundation of China (Grant No. 61333008) and Funds for Creative Research Groups of Hebei Normal University of Science and Technology (Grant No. CXTD2012-08). The author thanks Academician Hong-Xin WU of Chinese Academy of Sciences, for his guidance and valuable suggestions, and acknowledges helpful discussion with Dr. Yong-Jun LEI during the author’s postdoctoral research in Beijing Institute of Control Engineering, China Academy of Space Technology. The author is also grateful to the anonymous referees for their constructive comments and suggestions.

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Correspondence to Duoqing Sun.

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Sun, D. Stability analysis of golden-section adaptive control systems based on the characteristic model. Sci. China Inf. Sci. 60, 092205 (2017). https://doi.org/10.1007/s11432-016-9005-2

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Keywords

  • characteristic model
  • golden-section control law
  • stability
  • time-varying system
  • nonlinear system