Adaptive state-feedback stabilization for high-order stochastic non-linear systems with uncertain control coefficients

International Journal of Control

Volumn 80, Issue 9, 2007, Pages 1503-1516

  Tian, J ^a   Xie, X J ^a  

^a QUFU NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED LOOP SYSTEMS; CONTROL EQUIPMENT; NONLINEAR SYSTEMS; PROBABILITY; SYSTEM STABILITY;

ADAPTIVE STATE-FEEDBACK CONTROLLER; SUPPER BOUNDS; UNCERTAIN CONTROL COEFFICIENTS;

STOCHASTIC CONTROL SYSTEMS;

EID: 34648846696     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170701418917     Document Type: Article

References (28)

1. H. Deng and M. Krstić, "Stochastic nonlinear stabilization part I: a backstepping design", Sys. Cont. Lett., 32, pp. 143-150, 1997a.
2. H. Deng and. M. Krstić, "Stochastic nonlinear stabilization part II: inverse optimality", Sys. Cont. Lett., 32, pp. 151-159, 1997b.
3. H. Deng and M. Krstić, "Output-feedback stochastic nonlinear stabilization", IEEE Trans. Automat. Cont., AA, pp. 328-333, 1999.
4. H. Deng and M. Krstić, "Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance", Sys. Cont. Lett., 39, pp. 173-182, 2000.
5. H. Deng, M. Krstić and R. Williams, "Stabilization of stochastic nonlinear driven by noise of unknown covariance", IEEE Trans. Automat. Cont., 46, pp. 1237-1253, 2001.
6. R.Z. Has'minskii, Stochastic Stability of Differential Equations, Norwell, Massachusetts: Kluwer Academic Publishers, 1980.
7. M. Krstić and H. Deng, Stabilization of Uncertain Nonlinear Systems, New York: Springer, 1998.
8. H.J. Kushner, Stochastic Stability and Control, New York: Academic Press, 1967.
9. W. Lin and C Qian, "Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems", Sys. Cont. Lett., 39, pp. 339-351, 2000a.
10. W. Lin and C. Qian, "Adaptive regulation of high-order lower-triangular systems: an adding a power integrator technique", Sys. Cont. Lett., 39, pp. 353-364, 2000b.
11. W. Lin and C. Qian, "Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework", IEEE Trans. Automat. Com., 47, pp. 757-774, 2002a.
12. W. Lin and C. Qian, "Adaptive control of nonlinearly parameterized systems: the smooth feedback case", IEEE Trans. Automat. Cont., 47, pp. 1249-1266, 2002b.
13. Y. Liu, and J. Zhang, "Reduced-order observer-based control design for nonlinear stochastic systems", Sys. Cont. Lett., 52, pp. 123-135, 2004a.
14. Y. Liu and J. Zhang, "Minimal-order observer and output-feedback stabilization control design of stochastic nonlinear systems", Science in China (Ser. F), 47, pp. 527-544, 2004b.
15. Y. Liu and J. Zhang, "Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics", SIAM J. Cont. Optim., 45, pp. 885-926, 2006.
16. Y. Liu, Z.G. Pan and S. Shi, "Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitivie cost", IEEE Trans. Automat. Cont., 48, pp. 509-513, 2003a.
17. S.J. Liu, J.F. Zhang and Z.P. Jiang, "Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems", Automatica, 43, pp. 238-251, 2007.
18. Y. Liu, J. Zhang and Z.G. Pan, "Design of satisfaction output feedback controls for stochastic nonlinear systems under quadratic tracking risk-sensitive index", Science in China (Ser. F), 46, pp. 126-145, 2003b.
19. Z.G. Pan and T. Basar, "Adaptive controller design for tracking and disturbance attenuation in parametric-feedback nonlinear systems", IEEE Trans. Automat. Cont., 43, pp. 1066-1083, 1998.
20. Z.G. Pan and T. Basar, "Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion", SIAM J. Cont. Optim., 37, pp. 957-995, 1999.
21. Z.G. Pan, K. Ezal, A. Krener and P.V. Kokotović, "Backstepping design with local optimality matching", IEEE Trans. Automat. Com., 46, pp. 1014-1027, 2001a.
22. Z.G. Pan, Y. Liu and S. Shi, "Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics", Science in China (Ser. F), 44, pp. 292-308, 2001b.
23. C. Qian and W. Lin, "A continuous feedback, approach to global strong stabilization of nonlinear systems", IEEE Trans. Automat. Com., 46, pp. 1061-1079, 2001.
24. C. Qian and W. Lin, "Practical output tracking of nonlinear systems with uncontrollable unstable linearization", IEEE Trans. Automat. Com., 47, pp. 21-36, 2002.
25. C. Qian, W. Lin and W. P. Dayawansa, "Smooth feedback, global stabilization and disturbance attenuation of nonlinear systems with uncontrollable linearization", SIAM J. Cont. Optimiz., 40, pp. 191-210, 2001.
26. Z.J. Wu, X.J. Xie and S.Y. Zhang, "Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function", Int. J. Cont., 79, pp. 1635-1646, 2006.
27. Z.J. Wu, X.J. Xie and S.Y. Zhang, "Adaptive backstepping controller design using stochastic small-gain theorem", Automatica, 43, pp. 608-620, 2007.
28. X.J. Xie and J. Tian, "State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics", Int. J. Rob. Nonlin. Cont., in press (2007).