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Adaptive exponential stabilization for a class of stochastic nonholonomic systems. (English) Zbl 1421.93126

Summary: This paper investigates the adaptive stabilization problem for a class of stochastic nonholonomic systems with strong drifts. By using input-state-scaling technique, backstepping recursive approach, and a parameter separation technique, we design an adaptive state feedback controller. Based on the switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the states of closed-loop system are global bounded in probability.

MSC:

93D21 Adaptive or robust stabilization
93E15 Stochastic stability in control theory
93C10 Nonlinear systems in control theory
93B52 Feedback control
70F25 Nonholonomic systems related to the dynamics of a system of particles

References:

[1] Brockett, R. W.; Millman, R. S.; Sussmann, H. J., Differential Geometric Control Theory (1983), Basel, Switzerland: Birkhauser, Basel, Switzerland
[2] Sun, Z.; Ge, S. S.; Huo, W.; Lee, T. H., Stabilization of nonholonomic chained systems via nonregular feedback linearization, Systems and Control Letters, 44, 4, 279-289 (2001) · Zbl 0986.93016 · doi:10.1016/S0167-6911(01)00148-7
[3] Jiang, Z. P., Robust exponential regulation of nonholonomic systems with uncertainties, Automatica, 36, 2, 189-209 (2000) · Zbl 0952.93057 · doi:10.1016/S0005-1098(99)00115-6
[4] Xi, Z.; Feng, G.; Jiang, Z. P.; Cheng, D., Output feedback exponential stabilization of uncertain chained systems, Journal of the Franklin Institute, 344, 1, 36-57 (2007) · Zbl 1119.93057 · doi:10.1016/j.jfranklin.2005.10.002
[5] Zheng, X. Y.; Wu, Y. Q., Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts, Nonlinear Analysis: Theory, Methods and Applications, 70, 2, 904-920 (2009) · Zbl 1152.93048 · doi:10.1016/j.na.2008.01.037
[6] Gao, F. Z.; Yuan, F. S.; Yao, H. J., Robust adaptive control for nonholonomic systems with nonlinear parameterization, Nonlinear Analysis: Real World Applications, 11, 4, 3242-3250 (2010) · Zbl 1214.93038 · doi:10.1016/j.nonrwa.2009.11.019
[7] Krstic, M.; Deng, H., Stabilization of Nonlinear Uncertain Systems (1998), New York, NY, USA: Springer, New York, NY, USA · Zbl 0906.93001
[8] Deng, H.; Krstic, M.; Williams, R. J., Stabilization of stochastic nonlinear systems driven by noise of unknown covariance, Proceedings of the IEEE Transactions on Automatic Control, 46, 8, 1237-1253 (2001) · Zbl 1008.93068 · doi:10.1109/9.940927
[9] Yu, X.; Xie, X. J., Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics, Proceedings of the IEEE Transactions on Automatic Control, 55, 2, 304-320 (2010) · Zbl 1368.93584 · doi:10.1109/TAC.2009.2034924
[10] Xie, X. J.; Duan, N.; Yu, X., State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamics, Proceedings of the EEE Transactions on Automatic Control, 56, 8, 1921-1926 (2011) · Zbl 1368.93230 · doi:10.1109/TAC.2011.2135150
[11] Duan, N.; Xie, X. J., Further results on output-feedback stabilization for a class of stochastic nonlinear systems, Proceedings of the IEEE Transactions on Automatic Control, 56, 5, 1208-1213 (2011) · Zbl 1368.93533 · doi:10.1109/TAC.2011.2107112
[12] Yu, X.; Xie, X. J.; Wu, Y. Q., Decentralized adaptive output-feedback control for stochastic interconnected systems with stochastic unmodeled dynamic interactions, International Journal of Adaptive Control and Signal Processing, 25, 8, 740-757 (2011) · Zbl 1227.93109 · doi:10.1002/acs.1240
[13] Liu, L.; Xie, X. J., State-feedback stabilization for stochastic high-order nonlinear systems with SISS inverse dynamics, Asian Journal of Control, 14, 4, 1-11 (2012) · Zbl 1282.93209 · doi:10.1002/asjc.288
[14] Xie, X. J.; Liu, L., A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay, Proceedings of the IEEE Transactions on Automatic Control, 58, 2, 494-499 (2013) · Zbl 1369.93513
[15] Wu, Z. J.; Xia, Y. Q.; Xie, X. J., Stochastic barbalat’s lemma and its applications, Proceedings of the IEEE Transactions on Automatic Control, 57, 6, 1537-1543 (2012) · Zbl 1369.93707
[16] Qin, X. Y., State-feedback stablization for a class of high-order stochastic nonlinearsystems, Journal of Anhui University (Natural Science Edition), 36, 4, 7-12 (2012) · Zbl 1274.93274
[17] Wang, J.; Gao, H.; Li, H., Adaptive robust control of nonholonomic systems with stochastic disturbances, Science in China F, 49, 2, 189-207 (2006) · Zbl 1117.93027 · doi:10.1007/s11432-006-0189-5
[18] Gao, F. Z.; Yuan, F. S.; Yao, H. J., Adaptive Stabilization for a class of Stochastic Nonholonomic Systems with nonlinear parameterization, Proceedings of the 24th Chinese Control and Decision Conference (CCDC ’12)
[19] Liu, Y. L.; Wu, Y. Q., Output feedback control for stochastic nonholonomic systems with growth rate restriction, Asian Journal of Control, 13, 1, 177-185 (2011) · Zbl 1248.93137 · doi:10.1002/asjc.230
[20] Lin, W.; Qian, C., Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework, Proceedings of the IEEE Transactions on Automatic Control, 47, 5, 757-774 (2002) · Zbl 1364.93400 · doi:10.1109/TAC.2002.1000270
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