The problem of adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations is studied in this paper. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using the input-state scaling technique and an adaptive backstepping control approach. Then, by adopting the switching strategy to eliminate the phenomenon of uncontrollability, the proposed adaptive state-feedback controller can guarantee that the closed-loop system has an almost surely unique solution for any initial state, and the equilibrium of interest is globally asymptotically stable in probability. Finally, the simulation example shows the effectiveness of the proposed scheme.
BrockettRMillmanRSussmannH (1983) Differential Geometric Control Theory. Basel: Birkhauser.
2.
ChenWWuJJiaoL (2012) State-feedback stabilization for a class of stochastic time-delay nonlinear systems. International Journal of Robust and Nonlinear Control22(17): 1921–1937.
3.
DengHKrsticM (1997) Stochastic nonlinear stabilization-i: A backstepping design. Systems & Control Letters32(3): 143–150.
4.
DengHKrsticMWilliamsR (2001) Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Transactions on Automatic Control46(8): 1237–1253.
5.
DuQWangCWangG (2015a) Adaptive state-feedback stabilization of stochastic high-order nonholonomic systems with nonlinear parameterization. Transactions of the Institute of Measurement and Control37(4): 536–549.
6.
DuQWangCWangGZhangD (2015b) State-feedback stabilization for stochastic high-order nonholonomic systems with Markovian switching. Nonlinear Analysis: Hybrid Systems18: 1–14.
7.
DuanNXieX (2011) Further results on output-feedback stabilization for a class of stochastic nonlinear systems. IEEE Transactions on Automatic Control56(5): 1208–1213.
8.
FuJMaRChaiT (2015) Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica54: 360–373.
9.
FuYTianZShiS (2003) State feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Transactions on Automatic Control48(2): 282–286.
10.
FuYTianZShiS (2005) Output feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Transactions on Automatic Control50(6): 847–851.
11.
GaoFYuanFYaoH (2011) Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts. Applied Mathematical Modelling35(9): 4222–4233.
12.
HuaCGuanX (2004) Comments on state feedback stabilization for a class of stochastic time-delay nonlinear systems. IEEE Transactions on Automatic Control49(7): 12–16.
13.
JiaoTXuSWeiY, et al. (2014) Decentralized global stabilization for stochastic high-order feedforward nonlinear systems with time-varying delays. Journal of the Franklin Institute351(10): 4872–4891.
14.
KhasminskiiR (1980) Stochastic Stability of Differential Equations. Norwell: Kluwer Academic.
15.
LinWQianC (2000) Adding one power integrator: a tool for global stabilization of high-order lower triangular systems. Systems & Control Letters39(5): 339–351.
16.
LiuLYinSZhangL, et al. (2017) Improved results on asymptotic stabilization for stochastic nonlinear time-delay systems with application to a chemical reactor system. IEEE Transactions on Systems, Man, and Cybernetics, Systems47(1): 195–204.
17.
LiuSGeSZhangJ (2008) Adaptive output-feedback control for a class of uncertain stochastic nonlinear systems with time delays. International Journal of Control81(8): 1210–1220.
LiuZWuY (2018) Universal strategies to explicit adaptive control of nonlinear time-delay systems with different structures. Automatica89: 151–159.
20.
LiuZWuYSunZ (2017) Output feedback control for a class of high-order nonholonomic systems with complicated nonlinearity and time-varying delay. Journal of the Franklin Institute354(11): 4289–4310.
21.
MaoX (2007) Stochastic Differential Equations and Their Applications. Chichester: Horwood.
22.
MinHXuSZhangBMaQ (2019) Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application. Automatica102: 105–110.
23.
PanZBasarT (1999) Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion. SIAM Journal on Control and Optimization37(3): 957–995.
24.
QinXMinHF (2018) Further Results on Adaptive state-feedback stabilization for a class of stochastic nonholonomic systems with time delays. International Journal of Control, Automation, and Systems16(2): 640–648.
25.
SongZZhaiJZhuZ (2018) Global stabilization for switched stochastic nonlinear systems via unbounded time-varying scaling. Transactions of the Institute of Measurement and Control40(7): 2270–2277.
26.
WangHZhuQ (2018) Adaptive output feedback control of stochastic nonholonomic systems with nonlinear parameterization. Automatica98: 247–255.
27.
WangQWeiC (2007) Robust adaptive control of nonholonomic systems with nonlinear parameterization. Acta Automatic Sinica33(4): 399–403.
28.
WangTLuoXLiW (2017) Razumikhin-type approach on state-feedback of stochastic high-order nonlinear systems with time-varying delay. International Journal of Robust and Nonlinear Control27(16): 3124–3134.
29.
WuHJiangYZhangDGuoZ (2019) State-feedback stabilization of stochastic nonholonomic systems under arbitrary switchings with time-varying delays: Volume II. In: Proceedings of 2018 Chinese Intelligent Systems Conference, Wenzhou, China, pp. 407–413.
30.
WuYLiuZ (2015) Output feedback stabilization for time-delay nonholonomic systems with polynomial conditions. ISA Transactions58: 1–10.
31.
WuYWuY (2010) Robust stabilization of delayed nonholonomic systems with strong nonlinear drifts. Nonlinear Analysis: Real World Applications11(5): 3620–3627.
32.
XieXLiuL (2013) A homogeneous domination approach to state feedback for stochastic high-order nonlinear systems with time-varying delay. IEEE Transactions on Automatic Control2(58): 494–499.
33.
XieXZhaoCDuanN (2014) Further results on state feedback stabilization of stochastic high-order nonlinear system. Science China Information Sciences57(7):1–14.
34.
XieXZhangXZhangK (2016) Finite-time state feedback stabilization of stochastic high-order nonlinear feedforward systems. International Journal of Control89(7): 1332–1341.
35.
ZhangDWangCQiuJ (2012) State-feedback stabilization for stochastic nonholonomic systems with Markovian switching. Modeling Identification and Control16: 221–228.
36.
ZhangDWangCWeiG (2014) Output feedback stabilization for stochastic nonholonomic systems with nonlinear drifts and Markovian switching. Asian Journal of Control16(6): 1679–1692.
37.
ZhaiJKarimiH (2019) Global output feedback control for a class of nonlinear systems with unknown homogenous growth condition. International Journal of Robust and Nonlinear Control29(7): 2082–2095.
38.
ZhaoCXieX (2013) Output feedback stabilization using small-gain method and reduced-order observer of stochastic nonlinear systems. IEEE Transactions on Automatic Control58(2): 523–529.
39.
ZhaoYYuJWuY (2011) State-feedback stabilization for a class of more general high order stochastic nonholonomic systems. International Journal of Adaptive Control and Signal Processing25(8): 687–706.
40.
ZhuQHuangT (2020) Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion. Systems & Control Letters140: 1–9.
