Robust H∞ control for nonlinear stochastic systems: A sliding-mode approach

IEEE Transactions on Automatic Control

Volumn 53, Issue 7, 2008, Pages 1695-1701

  Niu, Yugang ^a   Ho, Daniel W C ^b   Wang, Xingyu ^a  

^a EAST CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Exogenous disturbance; H performance; Nonlinear stochastic systems; Sliding mode control

Indexed keywords

CONTROL SYSTEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); STOCHASTIC CONTROL SYSTEMS; STOCHASTIC PROGRAMMING;

CONTROLLED SYSTEMS; EXOGENOUS DISTURBANCE; NONLINEAR STOCHASTIC SYSTEMS; ROBUST H; SLIDING-MODE CONTROL; STOCHASTIC DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 52249107323     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.929376     Document Type: Article

References (22)

1. W. M. Wonham, "Random differential equations in control theory," in Probabilistic Methods in Applied Mathematics, A. T. B. Reid, Ed. New York: Academic, 1970, vol. 2.
2. P. Florchinger, "Lyapunov-like techniques for stochastic stability," SIAM J. Control Optimiz., vol. 33, pp. 1151-1169, 1995.
3. H. Deng and M. Krstic, "Output-feedback stochastic nonlinear stabilization," IEEE Trans. Autom. Control, vol. 44, no. 2, pp. 328-333, Feb. 1999.
4. Z. Pan and T. Basar, "Backstepping controller design for nonlinear stochastic systems under a risk-sensitive const," SIAM J. Control Optimiz., vol. 37, pp. 957-995, 1999.
5. H. Deng and M. Krstic, "Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance," Syst. Control Lett., vol. 39, pp. 173-182, 2000.
6. Y. Liu, Z. Pan, and S. Shi, "Output-feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost," IEEE Trans. Autom. Control, vol. 48, no. 3, pp. 509-513, Mar. 2003.
7. Y. Fu, Z. Tian, and S. Shi, "State feedback stabilization for a class of stochastic time-delay nonlinear systems," IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 282-286, Feb. 2003.
8. ∞ control with state-dependent noise.," IEEE Trans. Autom. Control, vol. 49, no. 1, pp. 45-57, Jan. 2004.
9. ∞ filtering for nonlinear stochastic systems," IEEE Trans. Signal Process., vol. 53, no. 2, pp. 589-598, Feb. 2005.
10. ∞-like control for nonlinear stochastic systems," Syst. Control Lett., vol. 55, pp. 247-257, 2006.
11. H. H. Choi, "An explicit formula of linear sliding surfaces for a class of uncertain dynamic system with mismatched uncertainties," Automatica, vol. 34, pp. 1015-1020, 1998.
12. R. El-khazali, "Variable structure robust control of uncertain time-delay systems," Automatica, vol. 34, pp. 327-332, 1998.
13. K.-Y. Chang and W.-J. Wang, "Robust covaxiance control for perturbed stochastic multivariable system via variable structure control," Syst. Control Lett., vol. 37, pp. 323-328, 1999.
14. Y. Niu, J. Lam, X. Wang, and D. W. C. Ho, "Sliding mode control for nonlinear state-delayed systems using neural network approximation," IEE Proc. Control Theory and Applic., vol. 150, pp. 233-239, 2003.
15. X.-G. Yan, C. Edwards, and S. K. Spurgeon, "Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback," Automatica, vol. 40, pp. 613-620, 2004.
16. X.-G. Yan, C. Edwards, and S. K. Spurgeon, "Output feedback sliding mode control for non-minimum phase systems with non-linear disturbance," Int. J. Control, vol. 77, pp. 1353-1361, 2004.
17. W.-J. Cao and J.-X. Xu, "Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems," IEEE Trans. Autom. Control, vol. 49, no. 8, pp. 1355-1360, Aug. 2004.
18. Y. Niu, D. W. C. Ho, and J. Lam, "Robust integral sliding mode control for uncertain stochastic systems with time-varying delay," Automatica, vol. 41, pp. 873-880, 2005.
19. R. Z. Khasminskii, Stochastic Stability of Differential Equations. Amsterdam, The Netherlands: Sijthoffand Noordhoff, 1980.
20. V. I. Uktin and J. X. Shi, "Integral sliding mode in systems operating under uncertainty conditions," in Proc. IEEE Conf. Decision and Control, Kobe, Japan, 1996, pp. 4591-4596.
21. V. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations. Dordrecht, The Netherlands: Kluwer, 1992.
22. D. Higham, "An algorithmic introduction to numerical simulation of stochastic differential equations," SIAM Rev., vol. 43, pp. 525-546, 2001.