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SCIENCE CHINA Information Sciences, Volume 59, Issue 7: 072202(2016) https://doi.org/10.1007/s11432-016-5571-3

Further results on quantized stabilization of nonlinear cascaded systems with dynamic uncertainties

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  • ReceivedMar 30, 2015
  • AcceptedAug 12, 2015
  • PublishedJun 13, 2016

Abstract

This article studies the quantized partial-state feedback stabilization of a class of nonlinear cascaded systems with dynamic uncertainties. Under the assumption that the dynamic uncertainties are input-to-state practically stable, a novel recursive design method is developed for quantized stabilization by taking into account the influence of quantization and using the small-gain theorem. When the dynamic uncertainty is input-to-state stable, asymptotic stabilization can be achieved with the proposed quantized control law.


Acknowledgment

Acknowledgments

This work was supported in part by National Science Foundation (Grant Nos. ECCS-1230040, ECCS-1501044), and National Natural Science Foundation of China (Grant Nos. 61374042, 61522305, 61533007), Fundamental Research Funds for the Central Universities (Grant Nos. N130108001, N140805001), and State Key Laboratory of Intelligent Control and Decision of Complex Systems.


References

[1] Kalman R E. Nonlinear aspects of sampled-data control systems. In: Proceedings of the Symposium on Nonlinear Circuit Theory, Brooklyn, 1956, 6: 273--313. Google Scholar

[2] Lunze J. Qualitative modelling of linear dynamical systems with quantized state measurements. Automatica, 1994, 30: 417 CrossRef Google Scholar

[3] Brockett R W, Liberzon D. Quantized feedback stabilization of linear systems. IEEE Trans Automat Contr, 2000, 45: 1279 CrossRef Google Scholar

[4] Liberzon D. Hybrid feedback stabilization of systems with quantized signals. Automatica, 2003, 39: 1543 CrossRef Google Scholar

[5] Tatikonda S, Mitter S. Control under communication constraints. IEEE Trans Automat Contr, 2004, 49: 1056 CrossRef Google Scholar

[6] Elia N, Mitter S K. Stabilization of linear systems with limited information. IEEE Trans Automat Contr, 2001, 46: 1384 CrossRef Google Scholar

[7] Fu M, Xie L. The sector bound approach to quantized feedback control. IEEE Trans Automat Contr, 2005, 50: 1698 CrossRef Google Scholar

[8] Liu J, Elia N. Quantized feedback stabilization of non-linear affine systems. Int J Contr, 2004, 77: 239 CrossRef Google Scholar

[9] de Persis C. $n$-bit stabilization of $n$-dimensional nonlinear systems in feedforward form. IEEE Trans Automat Contr, 2005, 50: 299 CrossRef Google Scholar

[10] Ceragioli F, de Persis C. Discontinuous stabilization of nonlinear systems: quantized and switching controls. Syst Contr Lett, 2007, 56: 461 CrossRef Google Scholar

[11] Liu T, Jiang Z P, Hill D J. Quantized stabilization of strict-feedback nonlinear systems based on {ISS} cyclic-small-gain theorem. Math Contr Signal Syst, 2012, 24: 75 CrossRef Google Scholar

[12] Liu T, Jiang Z P, Hill D J. A sector bound approach to feedback control of nonlinear systems with state quantization. Automatica, 2012, 48: 145 CrossRef Google Scholar

[13] Liu T, Jiang Z P, Hill D J. Nonlinear Control of Dynamic Networks. Boca Raton: CRC Press, 2014. Google Scholar

[14] Liu T, Jiang Z P, Hill D J. Quantized output-feedback control of nonlinear systems: a cyclic-small-gain approach. In: Proceedings of the 30th Chinese Control Conference, Yantai, 2011. 487--492. Google Scholar

[15] Liu T, Jiang Z P, Hill D J. Small-gain based output-feedback controller design for a class of nonlinear systems with actuator dynamic quantization. IEEE Trans Automat Contr, 2012, 57: 1326 CrossRef Google Scholar

[16] Jiang Z P, Liu T. Quantized nonlinear control---a survey. Acta Automat Sin, 2013, 39: 1820 Google Scholar

[17] Karafyllis I, Jiang Z P. Stability and Stabilization of Nonlinear Systems. London: Springer, 2011. Google Scholar

[18] Kokotović P V, Arcak M. Constructive nonlinear control: a historical perspective. Automatica, 2001, 37: 637 CrossRef Google Scholar

[19] Krstić M, Kanellakopoulos I, Kokotović P V. Nonlinear and Adaptive Control Design. Hoboken: John Wiley & Sons, 1995. Google Scholar

[20] Sontag E D. Input to state stability: basic concepts and results. In: Nonlinear and Optimal Control Theory. Berlin: Springer-Verlag, 2007. 163--220. Google Scholar

[21] Jiang Z P, Teel A R, Praly L. Small-gain theorem for {ISS} systems and applications. Math Contr Signal Syst, 1994, 7: 95 CrossRef Google Scholar

[22] Jiang Z P, Mareels I M Y. A small-gain control method for nonlinear cascade systems with dynamic uncertainties. IEEE Trans Automat Contr, 1997, 42: 292 CrossRef Google Scholar

[23] Barmish B R, Corless M, Leitmann G. A new class of stabilizing controllers for uncertain dynamical systems. SIAM J Contr Optim, 1983, 21: 246 CrossRef Google Scholar

[24] Byrnes C I, Priscoli F D, Isidori A. Output Regulation of Uncertain Nonlinear Systems. 1st ed. Boston:Birkh{ä}user, 1997. Google Scholar

[25] Chen Z, Huang J. Stabilization and Regulation of Nonlinear Systems: a Robust and Adaptive Approach. Berlin: Springer, 2015. Google Scholar

[26] Sun W J, Huang J. Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application. Sci China Ser F-Inf Sci, 2009, 52: 2172 Google Scholar

[27] Lin Z. Semi-global stabilization of linear systems with position and rate limited actuators. Syst Contr Lett, 1997, 30: 1 CrossRef Google Scholar

[28] Liu X M, Lin Z L. On semi-global stabilization of minimum phase nonlinear systems without vector relative degrees. Sci China Ser F-Inf Sci, 2009, 52: 2153 CrossRef Google Scholar

[29] Li T, Xie L. Distributed coordination of multi-agent systems with quantized-observer based encoding-decoding. IEEE Trans Automat Contr, 2012, 57: 3023 CrossRef Google Scholar

[30] Guo J, Zhao Y L. Identification of the gain system with quantized observations and bounded persistent excitations. Sci China Inf Sci, 2014, 57: 012205 Google Scholar

[31] Li T, Zhang J F. Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle. Sci China Ser F-Inf Sci, 2009, 52: 2089 CrossRef Google Scholar

[32] Guo Y Q, Gui W H, Yang C H. On the design of compensator for quantization-caused input-output deviation. Sci China Inf Sci, 2011, 54: 824 CrossRef Google Scholar

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