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Adaptive control with saturation-constrainted observations for drag-free satellites — a set-valued identification approach

Science China Information Sciences volume 64, Article number: 202202 (2021) Cite this article

Abstract

The high-accuracy drag-free control is one of the key technologies for gravity gradient satellites. Since the range of the gravity gradiometer is limited, the measurement is subject to the saturation constraint. This paper introduces a design method of the adaptive drag-free control law by employing the set-valued identification approach. By inserting several thresholds in the constrained interval, the output observation is transformed into the set-valued information under different thresholds, based on which and the weighted optimization technique the identification algorithm for the unknown parameter is constructed. The adaptive drag-free control law is designed via the certainty equivalence principle. It is shown that the identification algorithm is strongly convergent and the convergence rate of the estimation error is obtained. The performance of the closed-loop system is analyzed, and the asymptotic optimality of the adaptive controller is proved. The numerical simulation is included to verify the effectiveness of the main results.

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References

  1. Dittus H, Lammerzahl C, Turyshev S. Lasers, Clocks, and Drag-Free: Exploration of Relativistic Gravity in Space. Berlin: Springer, 2008

    Book  Google Scholar 

  2. Luo Z, Zhong M, Bian X, et al. Mapping Earth’s gravity in space: review and future perspective. Adv Mech, 2014, 44: 291–337

    Google Scholar 

  3. Lange B. The control and use of drag-free satellites. Dissertation for Ph.D. Degree. Stanford: Stanford University, 1964

    Google Scholar 

  4. Haines R. Development of a drag-free control system. In: Proceedings of the 14th Annual AIAA/USU Conference on Small Satellites, Utah, 2000

  5. Evers W. GOCE Dynamical Analysis and Drag-Free Mode Control. DCT Report, 2004

  6. Canuto E. Drag-free and attitude control for the GOCE satellite. Automatica, 2008, 44: 1766–1780

    MathSciNet  Article  Google Scholar 

  7. Prieto D, Bona B. Orbit and attitude control for the European satellite GOCE. In: Proceedings of IEEE Networking, Sensing and Control, Politecnico di Torino, 2005

  8. Wu S F, Fertin D. Spacecraft drag-free attitude control system design with quantitative feedback theory. Acta Astronaut, 2008, 62: 668–682

    Article  Google Scholar 

  9. Prieto D, Ahmad Z. A drag free control based on model predictive techniques. In: Proceedings of American Control Conference, Portland, 2005

  10. Yang F, Tan S, Xue W, et al. Extended state filtering with saturation-constrainted observations and active disturbance rejection control of position and attitude for drag-free satellites (in Chinese). Acta Autom Sin, 2020, 46: 2337–2349

    Google Scholar 

  11. Guo L, Chen H-F. The Aström-Wittenmark self-tuning regulator revisited and ELS-based adaptive trackers. IEEE Trans Automat Contr, 1991, 36: 802–812

    Article  Google Scholar 

  12. Arabi E, Yucelen T. Set-theoretic model reference adaptive control with time-varying performance bounds. Int J Control, 2019, 92: 2509–2520

    MathSciNet  Article  Google Scholar 

  13. Xiao S, Dong J. Robust adaptive fault-tolerant tracking control for uncertain linear systems with time-varying performance bounds. Int J Robust Nonlin Control, 2019, 29: 849–866

    MathSciNet  Article  Google Scholar 

  14. Casini M, Garulli A, Vicino A. Input design in worst-case system identification using binary sensors. IEEE Trans Automat Contr, 2011, 56: 1186–1191

    MathSciNet  Article  Google Scholar 

  15. Godoy B I, Goodwin G C, Agüero J C, et al. On identification of FIR systems having quantized output data. Automatica, 2011, 47: 1905–1915

    MathSciNet  Article  Google Scholar 

  16. Guo J, Diao J-D. Prediction-based event-triggered identification of quantized input FIR systems with quantized output observations. Sci China Inf Sci, 2020, 63: 112201

    MathSciNet  Article  Google Scholar 

  17. Zheng C, Li L, Wang L Y, et al. How much information is needed in quantized nonlinear control? Sci China Inf Sci, 2018, 61: 092205

    MathSciNet  Article  Google Scholar 

  18. Wang L Y, Zhang J F, Yin G G. System identification using binary sensors. IEEE Trans Automat Contr, 2003, 48: 1892–1907

    MathSciNet  Article  Google Scholar 

  19. Jing L D, Zhang J F. Tracking control and parameter identification with quantized ARMAX systems. Sci China Inf Sci, 2019, 62: 199203

    MathSciNet  Article  Google Scholar 

  20. Wang T, Bi W, Zhao Y, et al. Radar target recognition algorithm based on RCS observation sequence - set-valued identification method. J Syst Sci Complex, 2016, 29: 573–588

    MathSciNet  Article  Google Scholar 

  21. Wang L Y, Yin G G, Zhang J F, et al. System Identification with Quantized Observations. Boston: Birkhäuser, 2010

    Book  Google Scholar 

  22. You K. Recursive algorithms for parameter estimation with adaptive quantizer. Automatica, 2015, 52: 192–201

    MathSciNet  Article  Google Scholar 

  23. Lian Y, Luo Z, Weyer E, et al. Parameter estimation with binary observations of input and output signals. In: Proceedings of 2016 Australian Control Conference (AuCC), 2016. 226–231

  24. Colinet E, Juillard J. A weighted least-squares approach to parameter estimation problems based on binary measurements. IEEE Trans Automat Contr, 2010, 55: 148–152

    MathSciNet  Article  Google Scholar 

  25. Zhao Y L, Bi W J, Wang T. Iterative parameter estimate with batched binary-valued observations. Sci China Inf Sci, 2016, 59: 052201

    Article  Google Scholar 

  26. Guo J, Zhang J F, Zhao Y L. Adaptive tracking control of a class of first-order systems with binary-valued observations and time-varying thresholds. IEEE Trans Automat Contr, 2011, 56: 2991–2996

    MathSciNet  Article  Google Scholar 

  27. Guo J, Zhang J F, Zhao Y L. Adaptive tracking of a class of first-order systems with binary-valued observations and fixed thresholds. J Syst Sci Complex, 2012, 25: 1041–1051

    MathSciNet  Article  Google Scholar 

  28. Zhao Y L, Guo J, Zhang J F. Adaptive tracking control of linear systems with binary-valued observations and periodic target. IEEE Trans Automat Contr, 2013, 58: 1293–1298

    MathSciNet  Article  Google Scholar 

  29. Chen H-F. Stochastic Approximation and Its Application. Dordrecht: Kluwer Academic Publishers, 2002

    Google Scholar 

  30. Guo L. Time-Varying Stochastic Systems—Stability, Estimation and Control. Changchun: Jilin Science and Technolory Press, 1993

    Google Scholar 

  31. Chow Y S, Teicher H. Probability Theory: Independence, Interchangeability, Martingales. 2nd ed. New York: Springer-Verlag, 1997

    Book  Google Scholar 

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Acknowledgements

This work was supported by National Key Research and Development Program of China (Grant No. 2018YFA0703800) and National Natural Science Foundation of China (Grant Nos. 61773054, 62025306).

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Authors and Affiliations

  1. Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering, Beijing, 100190, China

    Shuping Tan

  2. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Jin Guo

  3. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yanlong Zhao & Jifeng Zhang

Authors
  1. Shuping Tan
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  2. Jin Guo
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  3. Yanlong Zhao
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  4. Jifeng Zhang
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Corresponding author

Correspondence to Jifeng Zhang.

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Tan, S., Guo, J., Zhao, Y. et al. Adaptive control with saturation-constrainted observations for drag-free satellites — a set-valued identification approach. Sci. China Inf. Sci. 64, 202202 (2021). https://doi.org/10.1007/s11432-020-3145-0

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  • DOI: https://doi.org/10.1007/s11432-020-3145-0

Keywords

  • drag-free satellite
  • saturation constraint
  • adaptive control
  • set-valued identification