Global stabilization for stochastic high-order nonlinear systems via unbounded time-varying scaling

In this paper, the problem of global exponential stabilization is investigated for a class of stochastic high-order nonlinear systems. In the presence of stochastic disturbance, unbounded time-varying scaling of states is employed. With the aid of the backstepping technique and stochastic stability theory, a state feedback controller is constructed to guarantee the closed-loop system exponentially stable in probability. A numerical example is presented to illustrate the validity of the proposed control method.

[1]  Liang Liu,et al.  A Homogeneous Domination Approach to State Feedback of Stochastic High-Order Nonlinear Systems With Time-Varying Delay , 2013, IEEE Transactions on Automatic Control.

[2]  James Lam,et al.  Stabilization for T-S model based uncertain stochastic systems , 2011, Inf. Sci..

[3]  Xue‐Jun Xie,et al.  Adaptive Output Feedback Control for Stochastic Nonlinear Systems , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[4]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

[5]  Xin Yu,et al.  Global state feedback stabilisation of stochastic high-order nonlinear systems with high-order and low-order nonlinearities , 2016, Int. J. Syst. Sci..

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

[7]  Junyong Zhai,et al.  Adaptive Output Feedback Control for a Class of Uncertain Stochastic Nonlinear Systems With Unknown Time‐Delays , 2015 .

[8]  Xiaoping Liu,et al.  Adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with non-lower triangular structure , 2016, Fuzzy Sets Syst..

[9]  D. Sondermann.  Introduction to stochastic calculus for finance , 2006 .

[10]  Rajeeva L. Karandikar,et al.  Introduction to stochastic calculus*** , 2018, Actuarial Finance.

[11]  Ji-Feng Zhang,et al.  Reduced-order observer-based control design for nonlinear stochastic systems , 2004, Syst. Control. Lett..

[12]  Xue‐Jun Xie,et al.  Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching , 2008, CCC 2008.

[13]  Junyong Zhai,et al.  Global finite-time stabilization for a class of stochastic nonlinear systems by dynamic state feedback , 2013, Kybernetika.

[14]  Junyong Zhai,et al.  Output feedback control for a class of stochastic high‐order nonlinear systems with time‐varying delays , 2014 .

[15]  Petar V. Kokotovic,et al.  A scaled feedback stabilization of power integrator triangular systems , 2005, Proceedings of the 2004 American Control Conference.