Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation

In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.

[1]  Sing Kiong Nguang,et al.  Stability Analysis of Genetic Regulatory Networks With General Random Disturbances , 2019, IEEE Transactions on NanoBioscience.

[2]  Shengyuan Xu,et al.  Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application , 2019, Autom..

[3]  Hongyi Li,et al.  Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone , 2019, Autom..

[4]  Shaocheng Tong,et al.  Fuzzy Adaptive Finite-Time Control Design for Nontriangular Stochastic Nonlinear Systems , 2019, IEEE Transactions on Fuzzy Systems.

[5]  Jing Zhang,et al.  Finite-time tracking control for stochastic nonlinear systems with full state constraints , 2018, Appl. Math. Comput..

[6]  Yongduan Song,et al.  Tracking control of uncertain nonlinear systems with deferred asymmetric time-varying full state constraints , 2018, Autom..

[7]  Shengyuan Xu,et al.  Composite-Observer-Based Output-Feedback Control for Nonlinear Time-Delay Systems With Input Saturation and Its Application , 2018, IEEE Transactions on Industrial Electronics.

[8]  Wenjie Si,et al.  Adaptive neural control for MIMO stochastic nonlinear pure-feedback systems with input saturation and full-state constraints , 2018, Neurocomputing.

[9]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems , 2017, IEEE Transactions on Cybernetics.

[10]  Lu Bai,et al.  Adaptive Neural Control of Uncertain Nonstrict-Feedback Stochastic Nonlinear Systems with Output Constraint and Unknown Dead Zone , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[11]  Wei Wang,et al.  Adaptive Tracking Control for a Class of Stochastic Uncertain Nonlinear Systems With Input Saturation , 2017, IEEE Transactions on Automatic Control.

[12]  Zhengrong Xiang,et al.  Finite-time stabilization of switched stochastic nonlinear systems with mixed odd and even powers , 2016, Autom..

[13]  S. Khoo,et al.  Continuous finite‐time state feedback stabilizers for some nonlinear stochastic systems , 2015 .

[14]  Hui Wang,et al.  Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form , 2015, Autom..

[15]  Shengyuan Xu,et al.  Exact tracking control of nonlinear systems with time delays and dead-zone input , 2015, Autom..

[16]  G. Song,et al.  Adaptive neural control of stochastic nonlinear systems with multiple time-varying delays and input saturation , 2014, Neural Computing and Applications.

[17]  Bing Chen,et al.  Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown input saturation , 2014, Inf. Sci..

[18]  Cong-Ran Zhao,et al.  A Combined Homogeneous Domination and Sign Function Approach to Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

[19]  Shaocheng Tong,et al.  Adaptive output feedback control for a class of nonlinear systems with full-state constraints , 2014, Int. J. Control.

[20]  Zhihong Man,et al.  Finite-time stabilization of stochastic nonlinear systems in strict-feedback form , 2013, Autom..

[21]  Bing Chen,et al.  Robust Adaptive Fuzzy Tracking Control for Pure-Feedback Stochastic Nonlinear Systems With Input Constraints , 2013, IEEE Transactions on Cybernetics.

[22]  Liang Liu,et al.  Further results on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay , 2012, Autom..

[23]  Zhihong Man,et al.  Finite-time stability and instability of stochastic nonlinear systems , 2011, Autom..

[24]  Keng Peng Tee,et al.  Control of nonlinear systems with time-varying output constraints , 2009, 2009 IEEE International Conference on Control and Automation.

[25]  Francis Eng Hock Tay,et al.  Barrier Lyapunov Functions for the control of output-constrained nonlinear systems , 2009, Autom..

[26]  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.

[27]  Wei Lin,et al.  Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization , 2005, IEEE Transactions on Automatic Control.

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

[29]  Ruth J. Williams,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[30]  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).

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

[32]  Shaocheng Tong,et al.  Adaptive control-based Barrier Lyapunov Functions for a class of stochastic nonlinear systems with full state constraints , 2018, Autom..

[33]  Songjiao Shi,et al.  State feedback stabilization for a class of stochastic time-delay nonlinear systems , 2003, IEEE Trans. Autom. Control..

[34]  H. Deng,et al.  Stochastic Nonlinear Stabilization|part I: a Backstepping Design Submitted to Systems and Control Letters , 1997 .

[35]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .