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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 361269, 18 pages
Finite-Time Stabilization of Stochastic Nonholonomic Systems and Its Application to Mobile Robot
School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, Henan Province, China
Received 19 July 2012; Accepted 27 September 2012
Academic Editor: Ahmed El-Sayed
Copyright © 2012 Fangzheng Gao and Fushun Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. W. Brockett, “Asymptotic stability andfeed back stabilization,” in Differential Geometric Control Theory, R. S. Millman and H. J. Sussmann, Eds., pp. 2961–2963, Birkhäauser, Boston, Mass, USA, 1983.
- A. Astolfi, “Discontinuous control of nonholonomic systems,” Systems & Control Letters, vol. 27, no. 1, pp. 37–45, 1996.
- W. L. Xu and W. Huo, “Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator,” Systems & Control Letters, vol. 41, no. 4, pp. 225–235, 2000.
- R. M. Murray and S. S. Sastry, “Nonholonomic motion planning: steering using sinusoids,” IEEE Transactions on Automatic Control, vol. 38, no. 5, pp. 700–716, 1993.
- Z.-P. Jiang, “Iterative design of time-varying stabilizers for multi-input systems in chained form,” Systems & Control Letters, vol. 28, no. 5, pp. 255–262, 1996.
- Y.-P. Tian and S. Li, “Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control,” Automatica, vol. 38, no. 8, pp. 1139–1146, 2002.
- I. Kolmanovsky and N. H. McClamroch, “Hybrid feedback laws for a class of cascade nonlinear control systems,” IEEE Transactions on Automatic Control, vol. 41, no. 9, pp. 1271–1282, 1996.
- Z.-P. Jiang, “Robust exponential regulation of nonholonomic systems with uncertainties,” Automatica, vol. 36, no. 2, pp. 189–209, 2000.
- Z. Xi, G. Feng, Z. P. Jiang, and D. Cheng, “A switching algorithm for global exponential stabilization of uncertain chained systems,” IEEE Transactions on Automatic Control, vol. 48, no. 10, pp. 1793–1798, 2003.
- S. S. Ge, Z. Wang, and T. H. Lee, “Adaptive stabilization of uncertain nonholonomic systems by state and output feedback,” Automatica, vol. 39, no. 8, pp. 1451–1460, 2003.
- Y.-G. Liu and J.-F. Zhang, “Output-feedback adaptive stabilization control design for non-holonomic systems with strong non-linear drifts,” International Journal of Control, vol. 78, no. 7, pp. 474–490, 2005.
- Z. Xi, G. Feng, Z. P. Jiang, and D. Cheng, “Output feedback exponential stabilization of uncertain chained systems,” Journal of the Franklin Institute, vol. 344, no. 1, pp. 36–57, 2007.
- X. Zheng and Y. Wu, “Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 2, pp. 904–920, 2009.
- F. Gao, F. Yuan, and H. Yao, “Robust adaptive control for nonholonomic systems with nonlinear parameterization,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 3242–3250, 2010.
- Z.-Y. Liang and C.-L. Wang, “Robust stabilization of nonholonomic chained form systems with uncertainties,” Acta Automatica Sinica, vol. 37, no. 2, pp. 129–142, 2011.
- J. Wang, H. Gao, and H. Li, “Adaptive robust control of nonholonomic systems with stochastic disturbances,” Science in China. Series F, vol. 49, no. 2, pp. 189–207, 2006.
- Y.-L. Liu and Y.-Q. Wu, “Output feedback control for stochastic nonholonomic systems with growth rate restriction,” Asian Journal of Control, vol. 13, no. 1, pp. 177–185, 2011.
- Y. Zhao, J. Yu, and Y. Wu, “State-feedback stabilization for a class of more general high order stochastic nonholonomic systems,” International Journal of Adaptive Control and Signal Processing, vol. 25, no. 8, pp. 687–706, 2011.
- S. P. Bhat and D. S. Bernstein, “Continuous finite-time stabilization of the translational and rotational double integrators,” IEEE Transactions on Automatic Control, vol. 43, no. 5, pp. 678–682, 1998.
- E. Moulay and W. Perruquetti, “Finite time stability and stabilization of a class of continuous systems,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1430–1443, 2006.
- E. Moulay and W. Perruquetti, “Finite time stability conditions for non-autonomous continuous systems,” International Journal of Control, vol. 81, no. 5, pp. 797–803, 2008.
- Y. Hong, Z.-P. Jiang, and G. Feng, “Finite-time input-to-state stability and applications to finite-time control design,” SIAM Journal on Control and Optimization, vol. 48, no. 7, pp. 4395–4418, 2010.
- Y. Hong, “Finite-time stabilization and stabilizability of a class of controllable systems,” Systems & Control Letters, vol. 46, no. 4, pp. 231–236, 2002.
- Y. Hong and J. Wang, “Finite time stabilization of a class of nonlinear systems,” Science China, vol. 35, pp. 663–672, 2005.
- X. Huang, W. Lin, and B. Yang, “Global finite-time stabilization of a class of uncertain nonlinear systems,” Automatica, vol. 41, no. 5, pp. 881–888, 2005.
- S. Li and Y.-P. Tian, “Finite-time stability of cascaded time-varying systems,” International Journal of Control, vol. 80, no. 4, pp. 646–657, 2007.
- X. Chang and Y. G. Liu, “Finite-time stabilization for a class of zero-dynamics uncertain nonlinear systems with adjustable-settling-time,” Control Theory and Applications, vol. 26, no. 4, pp. 358–364, 2009.
- Y. Hong, J. Wang, and Z. Xi, “Stabilization of uncertain chained form systems within finite settling time,” IEEE Transactions on Automatic Control, vol. 50, no. 9, pp. 1379–1384, 2005.
- J. Yin, S. Khoo, Z. Man, and X. Yu, “Finite-time stability and instability of stochastic nonlinear systems,” Automatica, vol. 47, no. 12, pp. 2671–2677, 2011.
- R. Situ, Theory of Stochastic Differential Equations with Jumps and Applications, Mathematical and Analytical Techniques with Applications to Engineering, Springer, New York, NY, USA, 2005.
- W. Chen and L. C. Jiao, “Finite-time stability theorem of stochastic nonlinear systems,” Automatica, vol. 46, no. 12, pp. 2105–2108, 2010.
- H. Liu and X. Mu, “A converse Lyapunov theorems for stochastic finite-time stability,” in Proceedings of the 30th Chinese Control Conference (CCC '11), pp. 1419–1423, 2011.
- W. Li, X.-J. Xie, and S. Zhang, “Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions,” SIAM Journal on Control and Optimization, vol. 49, no. 3, pp. 1262–1282, 2011.
- J. P. Hespanha, D. Liberzon, and A. S. Morse, “Towards the supervisory control of uncertain nonholonomic systems,” in Proceedings of the American Control Conference (ACC '99), pp. 3520–3524, San Diego, Calif, USA, 1999.