DOI QR코드

DOI QR Code

구조적 불확실성을 갖는 비선형 시스템의 역최적제어

Inverse optimal control of nonlinear systems with structural uncertainty

  • 발행 : 2009.10.31

초록

본 논문에서는 구조적 불확실성을 갖는 비선형 시스템에 대한 역 최적 제어를 고려하였다. 먼저 불확실성의 구조적 범위를 논의하고, 제어 Lyapunov 함수를 기초로, 불확실성을 가지는 비선형시스템에 대한 대역적 점근적 안정도를 제안하고 증명한다. 이로부터 역 최적 제어를 위한 최저의 제약조건을 유도하고 증명한다. 이 결과를 이용하여 불확실성을 갖는 비선형시스템에 적용하였으며, 제안된 방법의 효율성을 검증하기 위하여 시뮬레이션을 하였다.

In this paper, inverse optimal control for nonlinear systems with structural uncertainty is considered. The first, the bounded of structural uncertainty is introduced and based on the control Lyapunov function, a theorem for the globally asymptotic stability is presented. From this a less conservative condition for the inverse optimal control is derived. The result is used to design an inverse optimal controller for a class of nonlinear systems, that improves and extends the existing results. The class of nonlinear system considered is also enlarger. The simulation results show the effectiveness of the method.

키워드

참고문헌

  1. Kokotovic, P., and Arcak, M.: "Constructive nonlinear control. A historical perspective", Automatica, 37,(5), pp.637-662, 2001. https://doi.org/10.1016/S0005-1098(01)00002-4
  2. Artstein, Z.: "Stabilization with relaxed controls", Nonlinear Anal. Theory Methods Appl.,1983, 7, (11), pp.1163-1173. https://doi.org/10.1016/0362-546X(83)90049-4
  3. Sontag,E.D.: "A Lyapunov-like characterization of asymptotic controllability", SIAM J. Control Optim., 21, (3), pp.462-471, 1983. https://doi.org/10.1137/0321028
  4. Freeman, R.A., and Kokotovic, P.V.: "Inverse optimality in robust stabilization". SIAM J. Control Optim., 34, (4), pp.1365-1391, 1996. https://doi.org/10.1137/S0363012993258732
  5. Freeman, R.A., and Primbs, J.A.: "Control Lyapunov functions: new ideas from an old source". Proc. IEEE Decision and Control Conf., Kobe, Japan, pp.3926-3931, 1996. https://doi.org/10.1109/CDC.1996.577294
  6. Mei, S.W., Shen, T.L., Sun, Y.Z., and Lu, Q.: "Passivation control of nonlinear systems with disturbances", Control Theory and Appl., 16, (6), pp.797-806, 1999.
  7. Sontag, E.D.: "A universal construction of Artstein's theorem on nonlineal stabilization", Syst. Control Lett., 13, (2), pp.117-123, 1989. https://doi.org/10.1016/0167-6911(89)90028-5
  8. Lin, Y., and Sontag, E.D.: "A universal formula for stabilization with bounded control", Syst. Control Lett., 16, (5), pp.393-397, 1991. https://doi.org/10.1016/0167-6911(91)90111-Q
  9. Isidori, A.: "Nonlinear control systems" (Springer Verlag, Ner-York, USA, 1995, 3rd edn.)
  10. Sepulchre, R., Jankovic, M., and kokotovic, P.V.: "Constructive nonlinear control" (Springer Verlag, London, 1996)
  11. Freeman, R.A., and Kokotovic, P.V.: "Robust controlof nonlinear systems" (Birkhauser, Boston, MA, 1996)