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Keywords:
stochastic nonlinear systems; dynamic state transformation; finite-time stabilization
stochastic nonlinear systems; dynamic state transformation; finite-time stabilization
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.
References:
[1] Bhat, S. P., Bernstein, D. S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 (2000), 751-766. DOI 10.1137/S0363012997321358 | MR 1756893 | Zbl 0945.34039
[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 10.1016/j.automatica.2011.02.053 | MR 2889258
[3] Deng, H., Krstić, M.: Stochastic nonlinear stabilizationq,- I: A backstepping design. Syst. Control Lett. 32 (1997), 143-150. DOI 10.1016/S0167-6911(97)00068-6 | MR 1492434
[4] Isidori, A.: Nonlinear Control Systems. 3rd edition. Springer-Verlag, New York 1995. MR 1410988 | Zbl 0931.93005
[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 10.1016/j.automatica.2013.01.054 | MR 3044021
[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 10.1016/j.automatica.2011.01.084 | MR 2878346 | Zbl 1215.93146
[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 0833.93003
[10] Praly, L., Jiang, Z. P.: Linear output feedback with dynamic high gain for nonlinear systems. Systems Control Lett. 53 (2004), 107-116. DOI 10.1016/j.sysconle.2004.02.025 | MR 2091836 | Zbl 1157.93494
[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 10.1109/9.935058 | MR 1842139 | Zbl 1012.93053
[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 10.1109/TAC.2002.803542 | MR 1929946
[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 10.1093/imamci/dnr017 | MR 2863408 | Zbl 1245.93121
[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 10.3724/SP.J.1004.2008.01188 | MR 2482434
[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 10.1109/TAC.2010.2043004 | MR 2642085
[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 10.1002/rnc.1177 | MR 2354647 | Zbl 1127.93354
[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 10.1016/j.automatica.2011.08.050 | MR 2886936 | Zbl 1235.93254
[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 10.1049/iet-cta.2010.0294 | MR 2857747
[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 10.1002/rnc.1765 | MR 2970951
[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 10.1049/iet-cta.2010.0362 | MR 2866083
[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 10.1016/j.automatica.2011.07.014 | MR 2889447 | Zbl 1244.93142
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