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How much information is needed in quantized nonlinear control?

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Abstract

Quantization rate is a crucial measure of complexity in determining stabilizability of control systems subject to quantized state measurements. This paper investigates quantization complexity for a class of nonlinear systems which are subjected to disturbances of unknown statistics and unknown bounds. This class of systems includes linear stablizable systems as special cases. Two lower bounds on the quantization rates are derived which guarantee input-to-state stabilizability for continuous-time and sampled-data feedback strategies, respectively. Simulation examples are provided to validate the results.

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References

  1. Åström K J, Kumar P R. Control: a perspective. Automatica, 2014, 50: 3–43

    Article  MathSciNet  Google Scholar 

  2. Delchamps D F. Stabilizing a linear system with quantized state feedback. IEEE Trans Autom Control, 1990, 35: 916–924

    Article  MathSciNet  MATH  Google Scholar 

  3. De Persis C. Nonlinear stabilizability via encoded feedback: the case of integral ISS systems. Automatica, 2006, 42: 1813–1816

    Article  MATH  Google Scholar 

  4. De Persis C, Jayawardhana B. Coordination of passive systems under quantized measurements. SIAM J Control Optim, 2012, 50: 3155–3177

    Article  MathSciNet  MATH  Google Scholar 

  5. Elia N, Mitter S K. Stabilization of linear systems with limited information. IEEE Trans Autom Control, 2001, 46: 1384–1400

    Article  MathSciNet  MATH  Google Scholar 

  6. Fradkov A L, Andrievsky B, Ananyevskiy M S. Passification based synchronization of nonlinear systems under communication constraints and bounded disturbances. Automatica, 2015, 55: 287–293

    Article  MathSciNet  Google Scholar 

  7. Fu M Y, Xie L H. The sector bound approach to quantized feedback control. IEEE Trans Autom Control, 2005, 50: 1698–1711

    Article  MathSciNet  MATH  Google Scholar 

  8. Kameneva T, Nešić D. Input-to-state stabilization of nonlinear systems with quantized feedback. In: Proceedings of the 17th IFAC World Congress, Seoul, 2008. 12480–12485

    Google Scholar 

  9. Matveev A S, Savkin A V. Estimation and Control over Communication Networks. Boston: Birkhäuser, 2009

    MATH  Google Scholar 

  10. Wang L Y, Li C, Yin G G, et al. State observability and observers of linear-time-invariant systems under irregular sampling and sensor limitations. IEEE Trans Autom Control, 2011, 56: 2639–2654

    Article  MathSciNet  MATH  Google Scholar 

  11. Wong W S, Brockett R W. Systems with finite communication bandwidth constraints II: stabilization with limited information feedback. IEEE Trans Autom Control, 1999, 44: 1049–1053

    Article  MathSciNet  MATH  Google Scholar 

  12. Nair G N, Evans R J. Stabilization with data-rate-limited feedback: tightest attainable bounds. Syst Control Lett, 2000, 41: 49–56

    Article  MathSciNet  MATH  Google Scholar 

  13. Nair G N, Evans R J. Exponential stabilisability of finite-dimensional linear systems with limited data rates. Automatica, 2003, 39: 585–593

    Article  MathSciNet  MATH  Google Scholar 

  14. Tatikonda S, Mitter S. Control under communication constraints. IEEE Trans Autom Control, 2004, 49: 1056–1068

    Article  MathSciNet  MATH  Google Scholar 

  15. Liberzon D, Hespanha J P. Stabilization of nonlinear systems with limited information feedback. IEEE Trans Autom Control, 2005, 50: 910–915

    Article  MathSciNet  MATH  Google Scholar 

  16. Hayakawa T, Ishii H, Tsumura K. Adaptive quantized control for nonlinear uncertain systems. Syst Control Lett, 2009, 58: 625–632

    Article  MathSciNet  MATH  Google Scholar 

  17. Kang X L, Ishii H. Coarsest quantization for networked control of uncertain linear systems. Automatica, 2015, 51: 1–8

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu K, Fridman E, Johansson K H. Dynamic quantization of uncertain linear networked control systems. Automatica, 2015, 59: 248–255

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhou J, Wen C Y, Yang G H. Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal. IEEE Trans Autom Control, 2014, 59: 460–464

    Article  MathSciNet  MATH  Google Scholar 

  20. Nair G N, Evans R J. Stabilizability of stochastic linear systems with finite feedback data rates. SIAM J Control Optim, 2004, 43: 413–436

    Article  MathSciNet  MATH  Google Scholar 

  21. Sahai A, Mitter S. The necessity and sufficiency of anytime capacity for stabilization of a linear system over a noisy communication link—Part I: scalar systems. IEEE Trans Autom Control, 2006, 52: 3369–3395

    MATH  Google Scholar 

  22. Tatikonda S, Sahai A, Mitter S. Stochastic linear control over a communication channel. IEEE Trans Autom Control, 2004, 49: 1549–1561

    Article  MathSciNet  MATH  Google Scholar 

  23. Brockett R W, Liberzon D. Quantized feedback stabilization of linear systems. IEEE Trans Autom Control, 2000, 45: 1279–1289

    Article  MathSciNet  MATH  Google Scholar 

  24. Liberzon D, Nešić D. Input-to-state stabilization of linear systems with quantized state measurements. IEEE Trans Autom Control, 2007, 52: 767–781

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Chuang Zheng & Lin Li

  2. Department of Electrical and Computer Engineering, Wayne State University, Detroit, 48202, USA

    Leyi Wang

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

    Chanying Li

Authors
  1. Chuang Zheng
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  2. Lin Li
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  3. Leyi Wang
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  4. Chanying Li
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Correspondence to Chanying Li.

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Zheng, C., Li, L., Wang, L. et al. How much information is needed in quantized nonlinear control?. Sci. China Inf. Sci. 61, 092205 (2018). https://doi.org/10.1007/s11432-016-9172-4

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  • DOI: https://doi.org/10.1007/s11432-016-9172-4

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