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SCIENCE CHINA Information Sciences, Volume 60, Issue 9: 092205(2017) https://doi.org/10.1007/s11432-016-9005-2

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

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  • ReceivedSep 25, 2016
  • AcceptedNov 29, 2016
  • PublishedMay 19, 2017

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.


Funded by

National Nature Science Foundation of China(61333008)

Funds for Creative Research Groups of Hebei Normal University of Science and Technology(CXTD2012-08)


Acknowledgment

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.


References

[1] {Å}ström K J. Adaptive feedback control. Proc IEEE, 1987, 75: 185-217 CrossRef Google Scholar

[2] Wu H X, Hu J, Xie Y C. Characteristic model-based all-coefficient adaptive control method and its applications. IEEE Trans Syst Man Cybern Part C-Appl Rev, 2007, 37: 213-221 Google Scholar

[3] Gao S G, Dong H R, Ning B. Characteristic model-based all-coefficient adaptive control for automatic train control systems. Sci China Inf Sci, 2014, 57: 092201-221 Google Scholar

[4] Meng B, Wu H X, Lin Z L, et al. Characteristic model based control of the X-34 reusable launch vehicle in its climbing phase. Sci China Ser F-Inf Sci, 2009, 52: 2216-2225 Google Scholar

[5] Meng B, Wu H X. On characteristic modeling of a class of flight vehicles' attitude dynamics. Sci China Tech Sci, 2010, 53: 2074-2080 CrossRef Google Scholar

[6] Di L, Lin Z L. Control of a flexible rotor active magnetic bearing test rig: a characteristic model based all-coefficient adaptive control approach. Control Theory Tech, 2014, 12: 1-12 CrossRef Google Scholar

[7] Huang H, Zhang Z. Characteristic model-based $H_{2}$/$H_{\infty }$ robust adaptive control during the re-entry of hypersonic cruise vehicles. Sci China Inf Sci, 2015, 58: 012202-12 Google Scholar

[8] Xie Y C, Wu H X, Lv Z D. The all-coefficient adaptive control method and its application in spacecraft attitude control. Space Tech, 1996, 16: 331-336 CrossRef Google Scholar

[9] Qi C Z, Wu H X, Lv Z D. The study on the stability of all-coefficient golden section feedback control system. \linebreak In: Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, 2000. 5: 3168--3171. Google Scholar

[10] Sun D Q, Wu H X. Study on the stability of golden section adaptive control systems based on characteristic modeling. In: Proceedings of the 11th International Fuzzy Systems Association World Congress. Beijing: Tsinghua University Press {&} Springer, 2005. 174--178. Google Scholar

[11] Sun D Q. Stability analysis of the golden section adaptive control systems for attitude keeping of spacecraft with unknown parameters. Appl Mech Mater, 2011, 80--81: 1096-1102 CrossRef Google Scholar

[12] Wang Y. Stability analysis of characteristic model-based adaptive method for a class of minimum-phase nonlinear system (in Chinese). Control Theory Appl, 2012, 29: 1097-1107 Google Scholar

[13] Meng B, Wu H X. Convergence and stability of the golden-section control. J Astronautics, 2009, 30: 2128-2132 Google Scholar

[14] Lang S J, Gu X Y, Chai T Y. A multivariable generalized self-tuning controller with decoupling design. IEEE Trans Automat Control, 1986, 31: 474-477 CrossRef Google Scholar

[15] Ahn S M. Stability of a matrix polynomial in discrete systems. IEEE Trans Autom Control, 1982, 27: 1122-1124 CrossRef Google Scholar

[16] Sun D Q, Sun Z M. Asymptotic stability of the golden-section control law for multi-input and multi-output linear systems. J App Math, 2012, 2012: 1-11 Google Scholar

[17] Zhou C J, Shi Y F, Yang S H, et al. Characteristic model-based adaptive discrete-time sliding mode control for the swing arm in a fourier transform spectrometer. IEEE Trans Syst Man Cybern Part C-Appl Rev, 2012, 42: 1633-1643 Google Scholar

[18] Wu Y F, Wang Z H, Li Y Y, et al. Characteristic modeling and control of servo systems with backlash and friction. Math Probl Eng, 2014, 2014: 1-21 Google Scholar

[19] Chang R Y, Yang S Y, Wang M L. A new approach for parameter identification of time-varying systems via generalized orthogonal polynomials. Int J Control, 1986, 44: 1747-1755 CrossRef Google Scholar

[20] Guo L. Time-Varying Stochastic Systems---Stability, Estimation and Control (in Chinese). Changchun: Jilin Science and Technology Press, 1993. 62--64. Google Scholar

[21] Ionescu T. Hyperstability of linear time-varying discrete systems. IEEE Trans Autom Control, 1970, 15: 645-647 CrossRef Google Scholar

[22] Johansson R. Global Lyapunov stability and exponential convergence of direct adaptive control. Int J Control, 1989, 50: 859-869 CrossRef Google Scholar

[23] Fadeyev D K, Sominsky I S. Collection of Exercise Problems in Higher Algebra (in Chinese). Beijing: Higher Education Press, 1987. 60. Google Scholar

[24] Spong M W, Thorp J S, Kleinwaks J M. Robust microprocessor control of robot manipulators. Automatica, 1987, 23: 373-379 CrossRef Google Scholar

[25] Huang T Z. Estimation of $\| $A$^{-1}\| _{\infty }$ and the smallest singular value. Comput Math Appl, 2008, 55: 1075-1080 CrossRef Google Scholar

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