Adaptive finite‐time stabilization of nonlinearly parameterized systems subject to mismatching disturbances

This paper gives a first try to the finite‐time control for nonlinear systems with unknown parametric uncertainty and external disturbances. The serious uncertainties generated by unknown parameters are compensated by skillfully using an adaptive control technique. Exact knowledge of the upper bounds of the disturbances is removed by employing a disturbance observer–based control method. Then, based on the disturbance observer–based control, backstepping technique, finite‐time adaptive control, and Lyapunov stability theory, a composite adaptive state‐feedback controller is strictly designed and analyzed, which guarantees the closed‐loop system to be practically finite‐time stable. Finally, both the practical and numerical examples are presented and compared to demonstrate the effectiveness of the proposed scheme.

[1]  Shengyuan Xu,et al.  Practically Finite-Time Control for Nonlinear Systems With Mismatching Conditions and Application to a Robot System , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[2]  Shengyuan Xu,et al.  Further Results on Adaptive Stabilization of High-Order Stochastic Nonlinear Systems Subject to Uncertainties , 2020, IEEE Transactions on Neural Networks and Learning Systems.

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

[4]  Shengyuan Xu,et al.  Output-Feedback Control for Stochastic Nonlinear Systems Subject to Input Saturation and Time-Varying Delay , 2019, IEEE Transactions on Automatic Control.

[5]  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.

[6]  Changbin Yu,et al.  Tuning function design for nonlinear adaptive control systems with multiple unknown control directions , 2018, Autom..

[7]  Guang-Hong Yang,et al.  Event‐triggered adaptive backstepping control for parametric strict‐feedback nonlinear systems , 2018 .

[8]  Xing Fang,et al.  Novel disturbance-observer-based control for systems with high-order mismatched disturbances , 2018, Int. J. Syst. Sci..

[9]  Shengyuan Xu,et al.  Adaptive finite‐time stabilization of a class of quantized nonlinearly parameterized systems , 2017 .

[10]  Weisheng Chen,et al.  Global Finite-Time Adaptive Stabilization of Nonlinearly Parametrized Systems With Multiple Unknown Control Directions , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[11]  X. Zhang,et al.  Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique , 2017, Int. J. Syst. Sci..

[12]  Mingjie Cai,et al.  Adaptive Practical Finite-Time Stabilization for Uncertain Nonstrict Feedback Nonlinear Systems With Input Nonlinearity , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[13]  Lei Guo,et al.  Neural Network-Based DOBC for a Class of Nonlinear Systems With Unmatched Disturbances , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Lei Guo,et al.  Composite adaptive anti-disturbance control for MIMO nonlinearly parameterized systems with mismatched general periodic disturbances , 2017, Int. J. Comput. Math..

[15]  Xue-Jun Xie,et al.  Adaptive Finite-Time Stabilization of High-Order Nonlinear Systems with Dynamic and Parametric Uncertainties , 2016 .

[16]  Mingjie Cai,et al.  Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty , 2016 .

[17]  Weisheng Chen,et al.  Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions , 2016, Autom..

[18]  Kemei Zhang,et al.  Finite‐time output feedback stabilization of nonlinear high‐order feedforward systems , 2016 .

[19]  Tong Liu,et al.  Conditional Random Fields for Image Labeling , 2016 .

[20]  Wei Xing Zheng,et al.  Global output regulation for strict‐feedback nonlinear systems with mismatched nonvanishing disturbances , 2015 .

[21]  Kemei Zhang,et al.  A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system , 2015, Autom..

[22]  Shuzhi Sam Ge,et al.  Adaptive Neural Output Feedback Control of Uncertain Nonlinear Systems With Unknown Hysteresis Using Disturbance Observer , 2015, IEEE Transactions on Industrial Electronics.

[23]  Zhiyong Chen,et al.  A novel adaptive control approach for nonlinearly parameterized systems , 2015 .

[24]  Xinghuo Yu,et al.  Continuous Finite-Time Output Regulation for Disturbed Systems Under Mismatching Condition , 2015, IEEE Transactions on Automatic Control.

[25]  Shengyuan Xu,et al.  Asymptotic Tracking Control of Uncertain Nonlinear Systems With Unknown Actuator Nonlinearity , 2014, IEEE Transactions on Automatic Control.

[26]  Lei Guo,et al.  Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances , 2014, J. Frankl. Inst..

[27]  P. Olver.  Nonlinear Systems , 2013 .

[28]  Shihua Li,et al.  Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties , 2011 .

[29]  Yuanqing Xia,et al.  Attitude stabilization of rigid spacecraft with finite‐time convergence , 2011 .

[30]  Shengyuan Xu,et al.  Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance , 2010 .

[31]  Zhong-Ping Jiang,et al.  Finite-Time Input-to-State Stability and Applications to Finite-Time Control Design , 2010, SIAM J. Control. Optim..

[32]  Kyung-Soo Kim,et al.  Disturbance Observer for Estimating Higher Order Disturbances in Time Series Expansion , 2010, IEEE Transactions on Automatic Control.

[33]  Yasser Abdel-Rady Ibrahim Mohamed,et al.  Design and Implementation of a Robust Current-Control Scheme for a PMSM Vector Drive With a Simple Adaptive Disturbance Observer , 2007, IEEE Transactions on Industrial Electronics.

[34]  Zhong-Ping Jiang,et al.  Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties , 2006, IEEE Transactions on Automatic Control.

[35]  Yiguang Hong,et al.  Adaptive finite-time control of nonlinear systems with parametric uncertainty , 2006, IEEE Transactions on Automatic Control.

[36]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[37]  Gang Feng,et al.  A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[38]  Zhihong Man,et al.  Non-singular terminal sliding mode control of rigid manipulators , 2002, Autom..

[39]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework , 2002, IEEE Trans. Autom. Control..

[40]  Wei Lin,et al.  Practical output tracking of nonlinear systems with uncontrollable unstable linearization , 2002, IEEE Trans. Autom. Control..

[41]  Tsai-Yuan Lin,et al.  An H∞ design approach for neural net-based control schemes , 2001, IEEE Trans. Autom. Control..

[42]  Wei Lin,et al.  Adaptive regulation of high-order lower-triangular systems : an adding a power integrator technique , 2000 .

[43]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[44]  Georges Bastin,et al.  Backstepping technique extended to nonlinear parameterization , 1996 .

[45]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

[46]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[47]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[48]  Kouhei Ohnishi,et al.  Microprocessor-Controlled DC Motor for Load-Insensitive Position Servo System , 1985, IEEE Transactions on Industrial Electronics.

[49]  F. Browder.  Nonlinear functional analysis , 1970 .