Adaptive State-Feedback Stabilization of Stochastic High-Order Nonlinear Systems With Time-Varying Powers and Stochastic Inverse Dynamics

This article investigates adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear systems with unknown time-varying powers and stochastic inverse dynamics for the first time. The existence of stochastic inverse dynamics, unknown parameters, and time-varying powers makes stochastic high-order nonlinear systems essentially different from the related papers, which brings a series of obstacles to achieve the control objective. By virtue of the parameter separation principle, adaptive technique and some flexible algebraic methods, a novel adaptive state-feedback controller is designed to guarantee that the equilibrium of the closed-loop system is globally stable in probability. Finally, a simulation is provided to demonstrate the effectiveness of the control scheme.

[1]  Xue‐Jun Xie,et al.  State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems with Stochastic Inverse Dynamics , 2007, 2007 IEEE International Conference on Control and Automation.

[2]  T. Basar,et al.  Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[3]  I. Kolmanovsky,et al.  Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[4]  Guang‐Ju Li,et al.  Finite‐time output‐feedback stabilization of high‐order nonholonomic systems , 2019, International Journal of Robust and Nonlinear Control.

[5]  Yungang Liu,et al.  Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers , 2019, Autom..

[6]  Jian Zhang,et al.  Global regulation for a class of stochastic high-order nonlinear systems with multiple unknown control directions , 2018, Int. J. Control.

[7]  H. Kushner.  Stochastic Stability and Control , 2012 .

[8]  Xue-Jun Xie,et al.  Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable , 2009, Autom..

[9]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: the smooth feedback case , 2002, IEEE Trans. Autom. Control..

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

[11]  Kemei Zhang,et al.  Finite-Time Stabilization of Stochastic High-Order Nonlinear Systems With FT-SISS Inverse Dynamics , 2019, IEEE Transactions on Automatic Control.

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

[13]  V. Ugrinovskii.  Robust H∞ infinity control in the presence of stochastic uncertainty , 1998 .

[14]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[15]  Jie Tian,et al.  Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization , 2009, Autom..

[16]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[17]  Liang Liu,et al.  State-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power , 2010 .

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

[19]  Fuad E. Alsaadi,et al.  Adaptive partial-state feedback control for stochastic high-order nonlinear systems with stochastic input-to-state stable inverse dynamics , 2015, Autom..

[20]  Xin Yu,et al.  Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics , 2010, Autom..

[21]  Wei Lin,et al.  Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization , 2001 .

[22]  Xue-Jun Xie,et al.  Dynamic State Feedback Stabilization of Stochastic Cascade Nonlinear Time-Delay Systems With SISS Inverse Dynamics , 2019, IEEE Transactions on Automatic Control.