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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.10 P.1742~1747

http://doi.org/10.1631/jzus.2006.A1742


Stabilization of stochastic nonholonomic systems


Author(s):  KE Hai-sen, YE Xu-dong

Affiliation(s):  Department of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   kehaisen@zju.edu.cn

Key Words:  Time-varying technique, Nonholonomic, Backstepping, Stochastic


KE Hai-sen, YE Xu-dong. Stabilization of stochastic nonholonomic systems[J]. Journal of Zhejiang University Science A, 2006, 7(10): 1742~1747.

@article{title="Stabilization of stochastic nonholonomic systems",
author="KE Hai-sen, YE Xu-dong",
journal="Journal of Zhejiang University Science A",
volume="7",
number="10",
pages="1742~1747",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1742"
}

%0 Journal Article
%T Stabilization of stochastic nonholonomic systems
%A KE Hai-sen
%A YE Xu-dong
%J Journal of Zhejiang University SCIENCE A
%V 7
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%P 1742~1747
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1742

TY - JOUR
T1 - Stabilization of stochastic nonholonomic systems
A1 - KE Hai-sen
A1 - YE Xu-dong
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 10
SP - 1742
EP - 1747
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1742


Abstract: 
In this work, we investigate the stabilization control design of nonholonomic stochastic system in strict-feedback form. Under the condition of all states being available for feedback, a state feedback controller was developed via the stochastic Lyapunov-like theorem and backstepping design technique. The controllers guarantee all states of the closed-loop system are bounded in probability, and largely asymptotically stable when the stochastic disturbances equal to zero at the equilibrium point of the open-loop system. Besides, the time-varying technique was introduced to avoid the uncontrollable state of chained system.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[5] Ge, S.S., Wang, Z.P., Lee, T.H., 2003. Adaptive stabilization of uncertain nonholonomic systems by state and output feedback. Automatica, 39(8):1451-1460.

[6] Hu, Y.M., Ge, S.S., Su, C.Y., 2004. Stabilization of uncertain nonholonomic system via time-varying sliding mode control. IEEE Transactions on Automatic Control, 49(5):757-763.

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[8] Jiang, Z.P., Nijmeijer, H., 1999. A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Transactions on Automatic Control, 44(2):265-279.

[9] Ke, H.S., Ye, X.D., 2006. Robust adaptive controller design for a class of nonlinear systems with unknown high frequency gains. Journal of Zhejiang University SCIENCE A, 7(3):315-320.

[10] Kim, B., Tsiotras, P., 2002. Controllers for unicycle-type wheeled robots: theoretical results and experimental validation. IEEE Transactions on Robotics and Automation, 18(3):294-307.

[11] Liu, Y.G., Zhang, J.F., 2004. Reduced-order observer-based control design for nonlinear stochastic systems. System & Control Letters, 52(2):123-135.

[12] Mnif, F., 2004. Recursive Backstepping Stabilization of a Wheeled Mobile Robot. First International Symposium on Control Communications and Signal Processing. Hammamet, Tunisia, p.135-139.

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[14] Tian, Y.P., Li, S.H., 2002. Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control. Automatica, 38(7):1139-1146.

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