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SCIENCE CHINA Information Sciences, Volume 64 , Issue 1 : 112211(2021) https://doi.org/10.1007/s11432-019-2762-3

Adaptive control of nonlinear systems with severe uncertainties in the input powers

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  • ReceivedSep 19, 2019
  • AcceptedDec 26, 2019
  • PublishedDec 23, 2020

Abstract

In this study, we discuss global adaptive stabilization for a class of uncertain nonlinear systems.The input powers of the system are unknown, and the upper bound and the nonzero lower bound are not known in advance.This suggests that the system suffers from severe uncertainties with respect to the input powers when compared with the related literature, which would considerably challenge the control design. The switching-based strategy can compensate for severe system uncertainties, especially new types of uncertainties, including those associated with the input powers. Herein, a switching adaptive controller is successfully designed to ensure that the resulting closed-loop system states are globally bounded and ultimately converge to the origin (the equilibrium point). The proposed controller is extended to the systems with unknown control directions by redefining the involved switching sequences.A simulation example demonstrates the effectiveness of the proposed switching adaptive controller.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61873146, 61973186, 61603217, 61703237, 61821004), Key and Development Plan of Shandong Province (Grant No. 2019JZZY010433), Taishan Scholars Climbing Program of Shandong Province, and Fundamental Research Funds of Shandong University.


References

[1] Krstić M. Nonlinear and Adaptive Control Design. New York: Wiley, 1995. Google Scholar

[2] Lewis F L, Dawson D M, Abdallah C T. Robot Manipulator Control: Theory and Practice. Boca Raton: CRC Press, 2003. Google Scholar

[3] Alvarez-Ramirez J, Espinosa-Pérez G, Noriega-Pineda D. Current-mode control of DC-DC power converters: a backstepping approach. Int J Robust Nonlinear Control, 2003, 13: 421-442 CrossRef Google Scholar

[4] Yang Z J, Hara S, Kanae S. Robust output feedback control of a class of nonlinear systems using a disturbance observer. IEEE Trans Contr Syst Technol, 2011, 19: 256-268 CrossRef Google Scholar

[5] Rui C L, Reyhangolu M, Kolmanovsky I, et al. Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. In: Proceedings of 36th IEEE Conference on Decision and Control, San Diego, 1997. 3998--4003. Google Scholar

[6] Strogatz S H. Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering. Boulder: Westview Press, 2001. Google Scholar

[7] Qian C, Lin W. Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst Control Lett, 2001, 42: 185-200 CrossRef Google Scholar

[8] Man Y, Liu Y. Global output-feedback stabilization for high-order nonlinear systems with unknown growth rate. Int J Robust Nonlinear Control, 2017, 27: 804-829 CrossRef Google Scholar

[9] Sun Z Y, Shao Y, Chen C C. Fast finite-time stability and its application in adaptive control of high-order nonlinear system. Automatica, 2019, 106: 339-348 CrossRef Google Scholar

[10] Sun Z Y, Yun M M, Li T. A new approach to fast global finite-time stabilization of high-order nonlinear system. Automatica, 2017, 81: 455-463 CrossRef Google Scholar

[11] Sun Z, Liu Y. Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. Automatica, 2007, 43: 1772-1783 CrossRef Google Scholar

[12] Li F, Liu Y. Global practical tracking with prescribed transient performance for inherently nonlinear systems with extremely severe uncertainties. Sci China Inf Sci, 2019, 62: 022204 CrossRef Google Scholar

[13] Su Z, Qian C, Shen J. Interval homogeneity-based control for a class of nonlinear systems with unknown power drifts. IEEE Trans Automat Contr, 2017, 62: 1445-1450 CrossRef Google Scholar

[14] Man Y, Liu Y. Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers. Automatica, 2019, 100: 171-181 CrossRef Google Scholar

[15] Wang M, Liu Y, Man Y. Switching adaptive controller for the nonlinear systems with uncertainties from unknown powers. IEEE Trans Syst Man Cybern Syst, 2019, doi: 10.1109/TSMC.2018.2814345 CrossRef Google Scholar

[16] Fu J, Ma R, Chai T. Adaptive finite-time stabilization of a class of uncertain nonlinear systems via logic-based switchings. IEEE Trans Automat Contr, 2017, 62: 5998-6003 CrossRef Google Scholar

[17] Cheong S G, Back J, Shim H, et al. Non-smooth feedback stabilizer for strict-feedback nonlinear systems not even linearizable at the origin. In: Proceedings of 2005 American Control Conference, Portland, 2005. 1907--1912. Google Scholar

[18] Sun Z Y, Zhang C H, Wang Z. Adaptive disturbance attenuation for generalized high-order uncertain nonlinear systems. Automatica, 2017, 80: 102-109 CrossRef Google Scholar

[19] Miller D E, Davison E J. An adaptive controller which provides an arbitrarily good transient and steady-state response. IEEE Trans Automat Contr, 1991, 36: 68-81 CrossRef Google Scholar

[20] Morse A S. Control using logic-based switching. In: Trends in Control: A European Perspective, London, 1995. 69--113. Google Scholar

[21] Chen C C, Qian C, Lin X. Smooth output feedback stabilization for a class of nonlinear systems with time-varying powers. Int J Robust Nonlinear Control, 2017, 27: 5113-5128 CrossRef Google Scholar

[22] Min Y Y, Liu Y G. Barbălat lemma and its application in analysis of system stability. J Shandong Univ, 2007, 37: 51--55. Google Scholar

[23] Khalil H K. Nonlinear Systems 3rd ed. New Jersey: Prentice Hall, 2002. Google Scholar

[24] Huang Y, Liu Y. Switching event-triggered control for a class of uncertain nonlinear systems. Automatica, 2019, 108: 108471 CrossRef Google Scholar

[25] Chen J, Li Z, Ding Z. Adaptive output regulation of uncertain nonlinear systems with unknown control directions. Sci China Inf Sci, 2019, 62: 089205 CrossRef Google Scholar