An Estimation Approach to Robust Adaptive Control of Uncertain Nonlinear Systems with Dynamic Uncertainties

  • Ahn, Choon-Ki (School of Electrical Engineering, Korea University) ;
  • Kim, Beom-Soo (School of Electrical Engineering, Korea University) ;
  • Lim, Myo-Taeg (School of Electrical Engineering, Korea University)
  • Published : 2003.03.01

Abstract

In this paper, a novel estimation technique for a robust adaptive control scheme is presented for a class of uncertain nonlinear systems with a general set of uncertainty. For a class of introduced more extended semi-strict feedback forms which generalize the systems studied in recent years, a novel estimation technique is proposed to estimate the states of the fully nonlinear unmodeled dynamics without stringent conditions. With the introduction of powerful functions, the estimation error can be tuned to a desired small region around the origin via the estimator parameters. In addition, with some effective functions, a modified adaptive backstepping for dynamic uncertainties is presented to drive the output to an arbitrarily small region around the origin by an appropriate choice of the design parameters. With our proposed schemes, we can remove or relax the assumptions of the existing results.

Keywords

References

  1. Nonlinear Control Design: Geometric, Adaptive, and Robust R. Marino;P. Tomei
  2. Nonlinear and Adaptive Control Design M. Krstic;I. Kanellakopoulos;P. V. Kokotovic
  3. IEEE Trans. on Autom. Cont. v.36 Systematic design of adaptive controllers for feedback linearizable systems I. Kanellakopoulos;P. V. Kokotovic;A. S. Morse https://doi.org/10.1109/9.100933
  4. System & Control Letters v.19 Adaptive nonlinear control without over-parametrization M. Krstic;I. Kanellakopoulos;P. V. Kokotovic https://doi.org/10.1016/0167-6911(92)90111-5
  5. Foundations of Adaptive control Global Adaptive Observers and Output Feedback Stabilization for a Class of Nonlinear Systems R. Marino;P. Tomei
  6. IEEE Trans. on Autom. Cont. v.38 Global adaptive output feedback control of nonlinear systems, part I: Linear parametrization R. Marino;P. Tomei https://doi.org/10.1109/9.186309
  7. IEEE Trans. on Autom. Cont. v.38 Global adaptive output feedback control of nonlinear systems, part II: Nonlinear parametrization R. Marino;P. Tomei https://doi.org/10.1109/9.186310
  8. System & Control Letters v.17 Dynamic output feedback linearization and global stabilization R. Marino;P. Tomei https://doi.org/10.1016/0167-6911(91)90036-E
  9. IEEE Trans. on Autom. Cont. v.37 Global adaptive observers for nonlinear systems via filtered transformations R. Marino;P. Tomei https://doi.org/10.1109/9.151117
  10. Automatica v.32 Tracking controllers for system linear in the unmeasured states R. A. Freeman;P. V. Kokotovic https://doi.org/10.1016/0005-1098(95)00193-X
  11. Automatica v.34 Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties Z. Jiang;L. Praly https://doi.org/10.1016/S0005-1098(98)00018-1
  12. Proc. of IEEE CDC Robust adaptive control of systems with nonlinear unmodeled dynamics Z. P. Jiang;D. J. Hill;J. Chen
  13. Proc. of IEEE CDC Observer based adaptive robust control of a class of nonlinear systems with dynamic uncertainties L. Xu;B. Yao
  14. IEEE Trans. on Autom. Cont. v.44 A robust adaptive back-stepping scheme for nonlinear systems with unmodeled dynamics Z. Jiang;D. Hill https://doi.org/10.1109/9.788536
  15. IEEE Trans. on Autom. Cont. v.40 A new model for control of systems with friction C. Canudas de Wit;H. Olsson;K. J. Astrom;P. Lischinsky https://doi.org/10.1109/9.376053
  16. Nonlinear Dynamics v.10 Global stabilization of the oscillating eccentric rotor C. J. Wan;D. S. Bernstein;V. T. Coppola https://doi.org/10.1007/BF00114798
  17. Automatica v.33 Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form B. Yao;M. Tomizuka
  18. Proc. of IEEE CDC High performance adaptive robust control of nonlinear systems: a general framework and new schemes B. Yao
  19. Proc. of IEEE CDC Nonlinear bserver/controller design for a class of nonlinear systems Y. Tan;I. Kanellakopoulos;Z. Jiang
  20. Automatica v.32 A robust adaptive nonlinear control design M. M. Polycarpou;P. A. Ioannou https://doi.org/10.1016/0005-1098(95)00147-6