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Title: Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback (English)
Author: Ai, Weiqing
Author: Zhai, Junyong
Author: Fei, Shumin
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 49
Issue: 4
Year: 2013
Pages: 590-600
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: stochastic nonlinear systems
Keyword: dynamic state transformation
Keyword: finite-time stabilization
MSC: 62A10
MSC: 93E12
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Date available: 2013-09-17T16:29:52Z
Last updated: 2013-09-17
Stable URL: http://hdl.handle.net/10338.dmlcz/143447
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Reference: [1] Bhat, S. P., Bernstein, D. S.: Finite-time stability of continuous autonomous systems..SIAM J. Control Optim. 38 (2000), 751-766. Zbl 0945.34039, MR 1756893, 10.1137/S0363012997321358
Reference: [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. MR 2889258, 10.1016/j.automatica.2011.02.053
Reference: [3] Deng, H., Krstić, M.: Stochastic nonlinear stabilizationq,- I: A backstepping design..Syst. Control Lett. 32 (1997), 143-150. MR 1492434, 10.1016/S0167-6911(97)00068-6
Reference: [4] Isidori, A.: Nonlinear Control Systems..3rd edition. Springer-Verlag, New York 1995. Zbl 0931.93005, MR 1410988
Reference: [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. MR 3044021, 10.1016/j.automatica.2013.01.054
Reference: [6] Kristić, M., Deng, H.: Stabilization of uncertain systems..Springer-Verlag, New York 1998.
Reference: [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. Zbl 1215.93146, MR 2878346, 10.1016/j.automatica.2011.01.084
Reference: [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.
Reference: [9] Marino, R., Tomei, P.: Nonlinear Control Design..Prentice Hall, U.K. 1995. Zbl 0833.93003
Reference: [10] Praly, L., Jiang, Z. P.: Linear output feedback with dynamic high gain for nonlinear systems..Systems Control Lett. 53 (2004), 107-116. Zbl 1157.93494, MR 2091836, 10.1016/j.sysconle.2004.02.025
Reference: [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. Zbl 1012.93053, MR 1842139, 10.1109/9.935058
Reference: [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. MR 1929946, 10.1109/TAC.2002.803542
Reference: [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.
Reference: [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. Zbl 1245.93121, MR 2863408, 10.1093/imamci/dnr017
Reference: [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. MR 2482434, 10.3724/SP.J.1004.2008.01188
Reference: [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. MR 2642085, 10.1109/TAC.2010.2043004
Reference: [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. Zbl 1127.93354, MR 2354647, 10.1002/rnc.1177
Reference: [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. Zbl 1235.93254, MR 2886936, 10.1016/j.automatica.2011.08.050
Reference: [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. MR 2857747, 10.1049/iet-cta.2010.0294
Reference: [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. MR 2970951, 10.1002/rnc.1765
Reference: [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. MR 2866083, 10.1049/iet-cta.2010.0362
Reference: [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. Zbl 1244.93142, MR 2889447, 10.1016/j.automatica.2011.07.014
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