State-feedback stabilisation for stochastic non-holonomic systems with time-varying delays

This study investigates the problem of state-feedback stabilisation for a class of stochastic non-holonomic systems in chained form with time-varying delays. By using input-state-scaling technique and backstepping recursive approach, and choosing an appropriate Lyapunov–Krasoviskii functional, a state-feedback controller is constructed. Based on switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller could ensure that the closed-loop system is globally asymptotically regulated at origin in probability. A simulation example is provided to illustrate the effectiveness of the proposed method.

[1]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

[2]  T. Başar,et al.  Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion , 1999 .

[3]  Liang Liu,et al.  Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay , 2011, Autom..

[4]  Shuzhi Sam Ge,et al.  Adaptive stabilization of uncertain nonholonomic systems by state and output feedback , 2003, Autom..

[5]  Xin Yu,et al.  Output Feedback Regulation of Stochastic Nonlinear Systems With Stochastic iISS Inverse Dynamics , 2010, IEEE Transactions on Automatic Control.

[6]  Xue-Jun Xie,et al.  Adaptive backstepping controller design using stochastic small-gain theorem , 2007, Autom..

[7]  Wei Lin,et al.  Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback , 2004, IEEE Trans. Autom. Control..

[8]  Shuzhi Sam Ge,et al.  Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays , 2008, Int. J. Control.

[9]  Carlos Canudas de Wit,et al.  Theory of Robot Control , 1996 .

[10]  Linda Bushnell,et al.  Stabilization of multiple input chained form control systems , 1995 .

[11]  Xiuyun Zheng,et al.  Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts , 2009 .

[12]  Fangzheng Gao,et al.  Robust adaptive control for nonholonomic systems with nonlinear parameterization , 2010 .

[13]  Shuzhi Sam Ge,et al.  Stabilization of nonholonomic chained systems via nonregular feedback linearization , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[14]  Khac Duc Do,et al.  Adaptive global stabilization of nonholonomic systems with strong nonlinear drifts , 2002, Syst. Control. Lett..

[15]  Magdi S. Mahmoud,et al.  Switched Time-Delay Systems , 2010 .

[16]  Wang Jiang,et al.  Adaptive robust control of nonholonomic systems with stochastic disturbances , 2006 .

[17]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[18]  A. Astolfi.  Discontinuous control of nonholonomic systems , 1996 .

[19]  Weiliang Xu,et al.  Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator , 2000 .

[20]  Zhong-Ping Jiang,et al.  Robust exponential regulation of nonholonomic systems with uncertainties , 2000, Autom..

[21]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[22]  Zhong-Ping Jiang,et al.  Iterative design of time-varying stabilizers for multi-input systems in chained form , 1996 .

[23]  Zhong-Ping Jiang,et al.  Output feedback exponential stabilization of uncertain chained systems , 2007, J. Frankl. Inst..

[24]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  S. C. Tong,et al.  Adaptive Neural Network Decentralized Backstepping Output-Feedback Control for Nonlinear Large-Scale Systems With Time Delays , 2011, IEEE Transactions on Neural Networks.

[26]  Xiaowu Mu,et al.  Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts , 2011 .

[27]  Yuqiang Wu,et al.  State‐feedback stabilization for a class of more general high order stochastic nonholonomic systems , 2011 .

[28]  Magdi S. Mahmoud,et al.  Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays , 2009 .

[29]  Huijun Gao,et al.  New delay-dependent stability criterion for stochastic systems with time delays , 2008 .