International Journal of Control, Automation, and Systems

  • 제6권3호
  • /
  • Pages.364-377
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  • 2008
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  • 1598-6446(pISSN)
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  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

Locally Optimal and Robust Backstepping Design for Systems in Strict Feedback Form with $C^1$ Vector Fields

  • Back, Ju-Hoon (Department of Mechanical Engineering, Korea University) ;
  • Kang, Se-Jin (School of Electrical Engineering and Computer Science, Seoul National University) ;
  • Shim, Hyung-Bo (School of Electrical Engineering and Computer Science, Seoul National University) ;
  • Seo, Jin-Heon (School of Electrical Engineering and Computer Science, Seoul National University)
  • 발행 : 2008.06.30
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초록

Due to the difficulty in solving the Hamilton-Jacobi-Isaacs equation, the nonlinear optimal control approach is not very practical in general. To overcome this problem, Ezal et al. (2000) first solved a linear optimal control problem for the linearized model of a nonlinear system given in the strict-feedback form. Then, using the backstepping procedure, a nonlinear feedback controller was designed where the linear part is same as the linear feedback obtained from the linear optimal control design. However, their construction is based on the cancellation of the high order nonlinearity, which limits the application to the smooth ($C^{\infty}$) vector fields. In this paper, we develop an alternative method for backstepping procedure, so that the vector field can be just $C^1$, which allows this approach to be applicable to much larger class of nonlinear systems.

키워드

참고문헌

  1. Z. Artstein, "Stabilization with relaxed controls," Nonlinear Analysis, vol. 7, no. 11, pp. 1163-1173, 1983 https://doi.org/10.1016/0362-546X(83)90049-4
  2. K. Ezal, P. V. Kokotovic, A. R. Teel, and T. Başar, "Disturbance attenuating output-feedback control of nonlinear systems with local optimality," Automatica, vol. 37, no. 6, pp. 805-817, 2001 https://doi.org/10.1016/S0005-1098(01)00024-3
  3. K. Ezal, Z. Pan, and P. V. Kokotovic, "Locally optimal and robust backstepping design," IEEE Trans. on Automatic Control, vol. 45, no. 2, pp. 260-271, 2000 https://doi.org/10.1109/9.839948
  4. H. K. Khalil, Nonlinear Systems, Third Ed., Prentice-Hall, 2002
  5. D. E. Kirk, Optimal Control Theory: An Introduction, Prentice-Hall, 1970
  6. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995
  7. R. Sepulchre, M. Jankovic, and P. V. Kokotovic, Constructive Nonlinear Control, Springer-Verlag, 1997
  8. E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Second Ed., Springer-Verlag, 1997
  9. M. Spivak, A Comprehansive Introduction to Differential Geometry, Vol. I, Third Ed., Publish or Perish Inc., 1999
  10. A. R. Teel, "Asymptotic convergence from Lp stability," IEEE Trans. on Automatic Control, vol. 44, no. 11, pp. 2169-2170, 1999 https://doi.org/10.1109/9.802938
  11. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, 1996