전자공학회논문지SC (Journal of the Institute of Electronics Engineers of Korea SC)

대한전자공학회 (The Institute of Electronics and Information Engineers)
권호 표지

제어불가능 불안정 선형화를 가지는 비선형 시스템에 대한 다이나믹 안정화

Dynamic Stabilization for a Nonlinear System with Uncontrollable Unstable Linearization

  • Seo, Sang-Bo (ASRI, School of Electrical Engineering, Seoul National University) ;
  • Shim, Hyung-Bo (ASRI, School of Electrical Engineering, Seoul National University) ;
  • Seo, Jin-Heon (ASRI, School of Electrical Engineering, Seoul National University)
  • 발행 : 2009.07.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서 우리는 비선형 시스템에 대한 다이나믹 스무스 상태 궤환 안정화기를 설계한다. 이 시스템은 우반평면에 고유값이 존재함으로 제어불가능 모드를 가질 수 있다. 이 시스템을 지수적으로 안정화하기 위해서 우리는 추가 다이나믹스를 고려한 다이나믹 제어기를 제안한다. 추가 다이나믹스의 설계 후에 다이나믹 차수 보정법과 역진기법을 이용하여 안정화기와 미분 가능, positive definite, proper인 리아푸노프 함수를 설계한다. 설계된 제어기의 수렴성은 차수 지표자라는 새로운 개념의 도입으로 증명될 것이다.

In this paper, we design a dynamic state feedback smooth stabilizer for a nonlinear system whose Jacobian linearization may have uncontrollable mode because its eigenvalues are on the right half-plane. After designing an augmented system, a dynamic exponent scaling and backstepping enable one to explicitly design a smooth stabilizer and a continuously differentiable Lyapunov function which is positive definite and proper. The convergence of the designed controller is proved by the new notion 'degree indicator'.

키워드

참고문헌

  1. R.W. Brockett, Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, Birkauser, Basel, pp. 181-191, 1983
  2. M. Kawski, 'Stabilization of nonlinear systems in the plane', Systems and Control Lett., vol. 12, no. 2, pp. 169-175, 1989 https://doi.org/10.1016/0167-6911(89)90010-8
  3. M. Kawski, 'Homogeneous stabilizing feedback laws', Control Theory Adv. Technol., vol. 6, pp. 497-516, 1990
  4. W.P. Dayawansa, 'Recent advances in the stabilization problem for low dimensional systems', Proceedings of second IFAC Symposium on Nonlinear Control Systems Design Symposium, Bordeaux, pp. 1-8, 1992
  5. W.P. Dayawansa, C.F. Martin, G. Knowles, 'Asymptotic stabilization of a class of smooth two dimensional systems', SIAM J. Control Optim., vol. 28, pp. 1321-1349, 1990 https://doi.org/10.1137/0328070
  6. J.M. Coron, L. Praly, 'Adding an integrator for the stabilization problem', Systems and Control Lett., vol. 17, pp. 89-104, 1991 https://doi.org/10.1016/0167-6911(91)90034-C
  7. M. Tsinias, J. Tsinias, 'Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization', Systems and Control Lett., vol. 38, pp. 115-126, 1999 https://doi.org/10.1016/S0167-6911(99)00052-3
  8. W. Lin, C. Qian, 'Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems', Systems and Control Lett., vol. 28, pp. 339-351, 2000 https://doi.org/10.1016/S0167-6911(99)00115-2
  9. C. Qian, W. Lin, 'Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization', Systems and Control Lett., vol. 42, pp. 185 -200, 2001 https://doi.org/10.1016/S0167-6911(00)00089-X
  10. D.B. Dai, P.V. Kokotovi, 'A scaled feedback stabilization of power integrator triangular systems', Automatica, vol. 54, pp. 645-653, 2005 https://doi.org/10.1016/j.sysconle.2004.11.004
  11. H.K. Khalil, Nonlinear Systems, NJ: Prentice-Hall, 3rd edition, 2002
  12. S. Seo, H. Shim, J.H. Seo, 'Global finite-time stabilization of a nonlinear system using dynamic exponent scaling', Proc. 47th IEEE Conference on Decision and Control, Cancun, Mexico, pp. 3805- 3810, 2008 https://doi.org/10.1109/CDC.2008.4739026