Previous |  Up |  Next

Article

Title: Global output-feedback finite-time stabilization for a class of stochastic nonlinear cascaded systems (English)
Author: Lan, Qixun
Author: Niu, Huawei
Author: Liu, Yamei
Author: Xu, Huafeng
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 53
Issue: 5
Year: 2017
Pages: 780-802
Summary lang: English
.
Category: math
.
Summary: In this paper, the problem of global finite-time stabilization via output-feedback is investigated for a class of stochastic nonlinear cascaded systems (SNCSs). First, based on the adding a power integrator technique and the homogeneous domination approach, a global output-feedback finite-time control law is constructed for the driving subsystem. Then, based on homogeneous systems theory, it is shown that under some mild conditions the global finite- time stability in probability of the driving subsystem implies the global finite-time stability in probability of the whole SNCS. Finally, a simulation example is given to illustrate the effectiveness of the proposed control design approach. (English)
Keyword: stochastic nonlinear systems
Keyword: cascaded systems
Keyword: output-feedback stabilization
Keyword: finite-time control
MSC: 39A13
MSC: 68M15
idZBL: Zbl 06861624
idMR: MR3750103
DOI: 10.14736/kyb-2017-5-0780
.
Date available: 2018-02-26T11:40:53Z
Last updated: 2018-05-25
Stable URL: http://hdl.handle.net/10338.dmlcz/147093
.
Reference: [1] Chen, Z., Huang, J.: A Lyapunov's direct method for the global robust stabilization of nonlinear cascaded systems..Automatica 44 (2008), 745-752. MR 2527071, 10.1016/j.automatica.2007.06.027
Reference: [2] Deng, H., Kristic, M.: Output-feedback stochastic nonlinear stabilization..IEEE Trans. Automat. Control 44 (1999), 328-333. MR 1670006, 10.1109/9.746260
Reference: [3] Ding, S., Levant, A., Li, S.: Simple homogeneous sliding-mode controller..Automatica 67 (2016), 22-32. MR 3471745, 10.1016/j.automatica.2016.01.017
Reference: [4] Ding, S., Li, S., Zheng, W.: Nonsmooth stabilization of a class of nonlinear cascaded systems..Automatica 48 (2012), 2597-2606. MR 2961159, 10.1016/j.automatica.2012.06.060
Reference: [5] Ding, S., Wang, J., Zheng, W.: Second-order sliding mode control for nonlinear uncertain systems bounded by positive functions..IEEE Trans. Industrial Electronics 62 (2015), 5899-5909. 10.1109/tie.2015.2448064
Reference: [6] Du, H., He, Y., Cheng, Y.: Finite-time cooperative tracking control for a class of second-order nonlinear multi-agent systems..Kybernetika 49 (2013), 507-523. Zbl 1274.93008, MR 3117911
Reference: [7] Du, H., He, Y., Cheng, Y.: Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control..IEEE Trans. Circ. Syst. 61 (2014), 1778-1788. 10.1109/tcsi.2013.2295012
Reference: [8] Du, H., Wen, G., Cheng, Y., He, Y., Jia, Ruting: Distributed Finite-Time Cooperative Control of Multiple High-Order Nonholonomic Mobile Robots..IEEE Trans. Neu. Net. Lear. Sys. PP (2016), 99, 1-9. MR 3730916, 10.1109/tnnls.2016.2610140
Reference: [9] Du, H., Wen, G., Yu, X., Li, S., Chen, M.: Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer..Automatica 62 (2015), 236-242. MR 3423994, 10.1016/j.automatica.2015.09.026
Reference: [10] Duan, N., Xie, X.: Further results on output-feedback stabilization for a class of stochastic nonlinear systems..IEEE Trans. Automat. Control 56 (2011), 1208-1213. MR 2815932, 10.1109/tac.2011.2107112
Reference: [11] Hong, Y., Huang, J., Xu, Y.: On an output feedback finite-time stabilization problem..IEEE Trans. Automat. Control 46 (2001), 305-309. MR 1814578, 10.1109/9.905699
Reference: [12] Hong, Y., Jiang, Z., Feng, G.: Finite-time input-to-state stability and applications to finite-time control design..SIAM J. Control Optim. 48 (2010), 4395-4418. Zbl 1210.93066, MR 2665472, 10.1137/070712043
Reference: [13] Jiang, Z., Mareels, I.: A small-gain control method for nonlinear cascaded systems with dynamic uncertainties..IEEE Trans. Autom. Control 42 (1997), 292-308. Zbl 0869.93004, MR 1435820, 10.1109/9.557574
Reference: [14] Khoo, S., Yin, J., Man, Z., Yu, X.: 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: [15] Lan, Q., Li, S.: Global output-feedback stabilization for a class of stochastic nonlinear systems via sampled-data control..Int. J. Robust Nonlinear Control 27, 17, (2017), 3643-3658. MR 3733629, 10.1002/rnc.3758
Reference: [16] Lan, Q., Li, S., Khoo, S., Shi, P.: Global finite-tim stabilisation for a class of stochastic nonlinear systems by output feedback..Int. J. Control 83 (2015), 494-506. MR 3303717, 10.1080/00207179.2014.962766
Reference: [17] Lendek, Z., Babuska, R., Schutter, B.: Stability of cascaded fuzzy systems and observers..IEEE Trans. Fuzzy Syst. 17 (2009), 641-653. 10.1109/tfuzz.2008.924353
Reference: [18] Li, J., Qian, C., Ding, S.: Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems..Int. J. Control 83 (2010), 2241-2252. MR 2747289, 10.1080/00207179.2010.511658
Reference: [19] Li, S., Tian, Y.: Finite-time stability of cascaded time-varying systems..Int. J. Control 80 (2007), 646-657. Zbl 1117.93004, MR 2304124, 10.1080/00207170601148291
Reference: [20] Li, W., Xie, X., Zhang, S.: Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions..SIAM J. Control Optim. 49 (2011), 1262-1282. MR 2818881, 10.1137/100798259
Reference: [21] Liu, S., Zhang, J.: Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states..Int. J. Robust Nonlinear Control 18 (2008), 665-687. MR 2403891, 10.1002/rnc.1255
Reference: [22] Mao, X.: Stochastic Differential Equations and Their Applications. Second edition..Horwood Publishing 1997. MR 1475218
Reference: [23] Mazenc, F., Praly, L., Dayawansa, W.: Global stabilization by output feedback: examples and counterexamples..Syst. Control Lett. 23 (1994), 119-125. MR 1287604, 10.1016/0167-6911(94)90041-8
Reference: [24] Ou, M., Gu, S., Wang, X., Dong, K.: Finite-Time tracking control of multiple nonholonomic mobile robots with external disturbances..Kybernetika 49 (2013), 1049-1067. MR 3453685, 10.14736/kyb-2015-6-1049
Reference: [25] Rosier, L.: Homogeneous Lyapunov function for homogeneous continuous vector field..Syst. Control Lett. 19 (1992), 467-473. Zbl 0762.34032, MR 1195304, 10.1016/0167-6911(92)90078-7
Reference: [26] Sun, H., Hou, L., Zong, G.: Continuous finite time control for static var compensator with mismatched disturbances..Nonlinear Dynamics 85 (2016), 2159-2169. 10.1007/s11071-016-2821-2
Reference: [27] Sun, Z., Xue, L., Zhang, K.: A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system..Automatica 58 (2015), 60-66. MR 3355628, 10.1016/j.automatica.2015.05.005
Reference: [28] Sun, Z., Yun, M., Li, T.: A new approach to fast global finite-time stabilization of high-order nonlinear terms..Automatica 81 (2017), 455-463. MR 3654631, 10.1016/j.automatica.2017.04.024
Reference: [29] Qian, C., 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: [30] Qian, C., Lin, W.: Output feedback control for a class of nonlinear systems: a nonseparation principle paradigm..IEEE Trans. Automat. Control 47 (2002), 1710-1715. MR 1929946, 10.1109/9.935058
Reference: [31] Wu, Y., Gao, F., Liu, Z.: Finite-time state-feedback stabilisation of non-holonomic systems with low-order non-linearities..IET Control Theory Appl. 9 (2015), 1553-1560. MR 3381713, 10.1049/iet-cta.2014.1001
Reference: [32] Wei, Y., Zheng, W.: Finite-time stochastic stabilisation of Markovian jump non-linear quadratic systems with partially known transition probabilities..IET Control Theory Appl. 8 (2014), 311-318. MR 3204891, 10.1049/iet-cta.2013.0570
Reference: [33] Wu, Z., Xie, X., Shi, P., Xia, Y.: Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching..Automatica 45 (2009), 997-1004. MR 2535360, 10.1016/j.automatica.2008.12.002
Reference: [34] Wu, Y., Yu, J., Zhao, Y.: Output feedback regulation control for a class of cascaded nonlinear systems and its applications to fan speed control..Nonlinear Anal.: Real World Appl. 13 (2012), 1278-1291. MR 2863956, 10.1016/j.nonrwa.2011.10.005
Reference: [35] Yin, J., Khoo, S.: Conitniuous finite-time state feedback stabilizers for some nonlinear stochastic systems..Int. J. Robust Nonlinear Control 25 (2015), 1581-1600. MR 3361629, 10.1002/rnc.3161
Reference: [36] Yin, J., Khoo, S., Man, Z., Yu, X.: 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: [37] Zha, W., Zhai, J., Fei, S., Wang, Y.: Finite-time stabilization for a class of stochastic nonlinear systems via output feedback..ISA Trans. 53 (2014), 709-716. MR 2391591, 10.1016/j.isatra.2014.01.005
Reference: [38] Zhou, J., Wen, C., Li, T.: Adaptive output feedback control of uncertain nonlinear systems with hysteresis nonlinearity..IEEE Trans. Automat. Control 57 (2012), 2627-2633. MR 2991665, 10.1109/tac.2012.2190208
.

Files

Files Size Format View
Kybernetika_53-2017-5_3.pdf 532.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo