Geodesic
Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback
Kybernetika, Tome 49 (2013) no. 4, pp. 590-600 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This paper addresses the problem of global finite-time stabilization by dynamic state feedback for a class of stochastic nonlinear systems. Firstly, we show a dynamic state transformation, under which the original system is transformed into a new system. Then, a state feedback controller with a dynamic gain is designed for the new system. It is shown that global finite-time stabilization in probability for a class of stochastic nonlinear system under linear growth condition can be guaranteed by appropriately choosing design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design scheme.
This paper addresses the problem of global finite-time stabilization by dynamic state feedback for a class of stochastic nonlinear systems. Firstly, we show a dynamic state transformation, under which the original system is transformed into a new system. Then, a state feedback controller with a dynamic gain is designed for the new system. It is shown that global finite-time stabilization in probability for a class of stochastic nonlinear system under linear growth condition can be guaranteed by appropriately choosing design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design scheme.
Classification : 62A10, 93E12
Keywords: stochastic nonlinear systems; dynamic state transformation; finite-time stabilization 
@article{KYB_2013_49_4_a5,
     author = {Ai, Weiqing and Zhai, Junyong and Fei, Shumin},
     title = {Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback},
     journal = {Kybernetika},
     pages = {590--600},
     year = {2013},
     volume = {49},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a5/}
}
TY  - JOUR
AU  - Ai, Weiqing
AU  - Zhai, Junyong
AU  - Fei, Shumin
TI  - Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback
JO  - Kybernetika
PY  - 2013
SP  - 590
EP  - 600
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a5/
LA  - en
ID  - KYB_2013_49_4_a5
ER  - 
%0 Journal Article
%A Ai, Weiqing
%A Zhai, Junyong
%A Fei, Shumin
%T Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback
%J Kybernetika
%D 2013
%P 590-600
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a5/
%G en
%F KYB_2013_49_4_a5
Ai, Weiqing; Zhai, Junyong; Fei, Shumin. Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback. Kybernetika, Tome 49 (2013) no. 4, pp. 590-600. http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a5/

[1] Bhat, S. P., Bernstein, D. S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 (2000), 751-766. | DOI | MR | Zbl

[2] Chen, W. S., Jiao, L. C.: Authors' reply to “Comments on ‘finite-time stability theorem of stochastic nonlinear systems [Automatica 46(2010)2105-2108]’”. Automatica 47 (2011), 1544-1545. | DOI | MR

[3] Deng, H., Krstić, M.: Stochastic nonlinear stabilizationq,- I: A backstepping design. Syst. Control Lett. 32 (1997), 143-150. | DOI | MR

[4] Isidori, A.: Nonlinear Control Systems. 3rd edition. Springer-Verlag, New York 1995. | MR | Zbl

[5] Khoo, S. Y., Yin, J. L., Man, Z. H., Yu, X. H.: Finite-time stabilization of stochastic nonlinear systems in strict-feedback form. Automatica 49 (2013), 1403-1410. | DOI | MR

[6] Kristić, M., Deng, H.: Stabilization of uncertain systems. Springer-Verlag, New York 1998.

[7] Li, W. Q., Jing, Y. W., Zhang, S. Y.: Adaptive state-feedback stabilization for a large class of high-order stochastic nonlinear systems. Automatica 47 (2011), 819-828. | DOI | MR | Zbl

[8] Li, W. Q., Jing, Y. W., Zhang, S. Y., Dimirovski, G. M.: State-feedback stabilization for high-order stochastic nonlinear systems without strict triangular conditions. In: Proc. Amer. Control Conference 2010, pp. 367-372.

[9] Marino, R., Tomei, P.: Nonlinear Control Design. Prentice Hall, U.K. 1995. | Zbl

[10] Praly, L., Jiang, Z. P.: Linear output feedback with dynamic high gain for nonlinear systems. Systems Control Lett. 53 (2004), 107-116. | DOI | MR | Zbl

[11] Qian, C. J., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Automat. Control 46 (2001), 1061-1079. | DOI | MR | Zbl

[12] Qian, C. J., Lin, W.: Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm. IEEE Trans. Automat. Control 47 (2002), 1710-1715. | DOI | MR

[13] Seo, S., Shim, H., Seo, J.: Global finite-time stabilization of a nonlinear system using dynamic exponent scaling. In: Proc. 47th IEEE Conference on Decision Control 2008, pp. 3805-3810.

[14] Seo, S., Shim, H., Seo, J.: Finite-time stabilizing dynamic control of uncertain multi-input linear systems. IMA J. Math. Control Inform. 28 (2011), 525-537. | DOI | MR | Zbl

[15] Tian, J., Xie, X.J.: Adaptive state-feedback stabilization for more general high-order stochastic nonlinear systems. Acta Autom. Sinica 34 (2008), 1188-1192. | DOI | MR

[16] Xie, X. J., Duan, N.: Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system. IEEE Trans. Automat. Control 55 (2010), 1197-1202. | DOI | MR

[17] Xie, X. J., Tian, J.: State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics. Internat. J. Robust. Nonlinear Control 17 (2007), 1343-1362. | DOI | MR | Zbl

[18] Yin, J. L., Khoo, S. Y., Man, Z. H., Yu, X. H.: Finite-time stability and instability of stochastic nonlinear systems. Automatica 47 (2011), 2671-2677. | DOI | MR | Zbl

[19] Zhai, J. Y., Fei, S. M.: Global practical tracking control for a class of uncertain non-linear systems. IET Control Theory Appl. 5 (2011), 1343-1351. | DOI | MR

[20] Zhai, J. Y., Qian, C. J.: Global control of nonlinear systems with uncertain output function using homogeneous domination approach. Internat. J. Robust Nonlinear Control 22 (2012), 1543-1561. | DOI | MR

[21] Zhang, X., Feng, G.: Global finite-time stabilisation of a class of feedforward non-linear systems. IET Control Theory Appl. 5 (2011), 1450-1457. | DOI | MR

[22] Zhang, X., Feng, G., Sun, Y.: Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems. Automatica 48 (2012), 499-504. | DOI | MR | Zbl