Title:
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Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback (English) |
Author:
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Ai, Weiqing |
Author:
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Zhai, Junyong |
Author:
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Fei, Shumin |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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49 |
Issue:
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4 |
Year:
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2013 |
Pages:
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590-600 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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stochastic nonlinear systems |
Keyword:
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dynamic state transformation |
Keyword:
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finite-time stabilization |
MSC:
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62A10 |
MSC:
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93E12 |
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Date available:
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2013-09-17T16:29:52Z |
Last updated:
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2013-09-17 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/143447 |
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Reference:
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[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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