Robust Adaptive Control for a Class of Nonlinear Systems with Complex Uncertainties



Seo, Sang-Bo;Back, Ju-Hoon;Shim, Hyung-Bo;Seo, Jin-H.

  • 발행 : 2009.06.30


This paper considers a robust adaptive stabilization problem for a class of uncertain nonlinear systems which include an unknown virtual control coefficient, an unknown constant parameter, and a time-varying disturbance whose bound is unknown, We propose a new estimator for an un-known virtual control coefficient and present a robust adaptive backstepping design procedure which results in a smooth state feedback control law, a new two-dimensional parameter update law, and a $C^1$ Lyapunov function which is positive definite and proper.


Robust control;Adaptive backstepping;Unknown virtual coefficient;Nonlinear parameterization


  1. R. Nussbaum, 'Somε remarks on a conjecture in parameter adaptive control', Systems & Control Letters, vol. 3, no. 5, pp. 243-246, 1983
  2. D. Mudgett and A. Morse, 'Adaptivε stabi1ization of 1inear systems with unknown high frequεncy gains' , IEEE Trans. Automat. Contr., vol. 30, no. 6, pp. 549-554, 1985
  3. B. Martensson, 'The order of any stabilizing regu1ator is sufficient a priori information for adaptivε stabilization', Systems & Control Letters, vol. 6, no. 2, pp. 87-91, 1985
  4. M. Fu and B. Barmish, 'Adaptive stabi1ization of linear systems via switching control', IEEE Trans. Automat. Contr., vol. 31 , no. 12, pp. 1097-1103, 1986
  5. R. Lozano and R. G. Moctezuma, 'Model reference adaptive control with unknown high frequency gain sign', Automatica, vol. 29, No. 6, pp. 1565-1569, 1993
  6. D. A. Suarez and R. Lozano, 'Adaptive control of nonminimum phase systems su이 ect to unknown bounded disturbances', IEEE Trans. Automat. Contr., vol. 41 , no. 12, pp. 1830-1836, 1996
  7. B. Martensson, 'Remarks on adaptivε stabilization of first ordεr non-linεar systems', Systems & ControlLetters, vol. 14, no.l , pp.1-7, 1990
  8. R. Lozano and B. Brogliato, 'Adaptive control of a simple non1inear system without a priori information on the p1ant parameters', IEEE Trans. Automat. Contr., vol. 37 no. 1, pp. 30-37, 1992
  9. X. D. Ye and J. P. Jiang, 'Adaptive non1inear design without a priori know1edge of control directions', IEEE Trans. Aμtomat. Contr., vol. 43, no. 11, pp. 1617-1621, 1998
  10. Z. Ding, 'Adaptive control of non1inear systems with unknown virtual control coefficients' , Int. J. Adαiptive Control Signal Proc., vol.14, no. 5, pp. 505-517, 2000<505::AID-ACS610>3.0.CO;2-N
  11. M. Krstic , J. Kanεllakopuolos, and P. V Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995
  12. A. M. Annaswamy, F. P. Skantze, and A. Loh, 'Adaptivε control of continuous time systems with convex/concave paramεterization,' Automatica, vol. 34, no.1, pp. 33-49, 1998
  13. R. Marino and P. Tomei, 'Adaptive output feedback regu1ation with almost disturbance decoupling for nonlinearly parameterized systems' , Int. J. Robust and Nonlinear Contr., vol. 10, no. 8, pp. 655-669, 2000<655::AID-RNC504>3.0.CO;2-Q
  14. W. Lin and C. Qian, 'Adaptive regu1ation of cascade systεms with nonlinεarlyparameterization' , Int. J. Robust and Nonlinear Contr., vol. 12, no. 12, pp. 1093-1108, 2002
  15. W. Lin and C. Qian, 'Adaptivε control of nonlinearly parameterized systems: The smooth feedback case' , IEEE Trans. Automat. Contr., vol. 47, no. 8, pp.1249-1266, 2002
  16. R. Marino and P. Tomei, Nonlinear Control Design, PrentIce Hall, U.K, 1995
  17. Z. P. Jiang and L. Pra1y, 'Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties', Automatica, vol. 34, no. 7, pp. 825-840, 1998
  18. W. Lin and C. Qian, 'Robust regu1ation of a chain of power integrators perturbed by a lower-triangu1ar vector fie1d', Int. J Robust and Nonlinear Contr., vol.. 10, no. 5, pp. 397-421, 2000<397::AID-RNC477>3.0.CO;2-N

피인용 문헌

  1. 1. Performance analysis of an adaptive feedback active noise control based earmuffs system vol.96, 2015, doi:10.5370/JEET.2009.4.2.292
  2. 2. Adaptive Control of Pitch Angle of Wind Turbine using a Novel Strategy for Management of Mechanical Energy Generated by Turbine in Different Wind Velocities vol.8, pp.4, 2013, doi:10.5370/JEET.2009.4.2.292