Adaptive finite‐time control for high‐order nonlinear systems with mismatched disturbances

Summary In this paper, adaptive finite-time control is addressed for a class of high-order nonlinear systems with mismatched disturbances. An adaptive finite-time controller is designed in which variable gains are adjusted to ensure finite-time stabilization for the closed-loop system. Chattering is reduced by a designed adaptive sliding mode observer which is also used to deal with the mismatched disturbances in finite time. The proposed adaptive finite-time control method avoids calculating derivative repeatedly of traditional backstepping methods and reduces computational burden effectively. Three numerical examples are given to illustrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

[1]  P. KRISHNAMURTHY,et al.  On Uniform Solvability of Parameter-Dependent Lyapunov Inequalities and Applications to Various Problems , 2006, SIAM J. Control. Optim..

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

[3]  R. Malhamé,et al.  Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system , 1985 .

[4]  Yuanqing Xia,et al.  Observer-based sliding mode control for a class of discrete systems via delta operator approach , 2010, J. Frankl. Inst..

[5]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[6]  Juntao Fei,et al.  Adaptive nonsingular terminal sliding mode control of MEMS gyroscope based on backstepping design , 2015 .

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

[8]  Yuanqing Xia,et al.  Evaluation and design of actuator fault diagnosability for nonlinear affine uncertain systems with unknown indeterminate inputs , 2017 .

[9]  Lei Guo,et al.  Composite disturbance‐observer‐based control and H∞ control for complex continuous models , 2010 .

[10]  Wu Yuqiang,et al.  Adaptive control of stochastic nonlinear systems with uncontrollable linearization , 2009 .

[11]  Yuri Shtessel,et al.  Adaptive dual layer second-order sliding mode control and observation , 2015, 2015 American Control Conference (ACC).

[12]  Zhiyong Dai,et al.  Backstepping dynamic surface control for a class of non-linear systems with time-varying output constraints , 2015 .

[13]  Haoyong Yu,et al.  Online data‐driven composite adaptive backstepping control with exact differentiators , 2016 .

[14]  Ligang Wu,et al.  Event-Triggered Fault Detection of Nonlinear Networked Systems , 2017, IEEE Transactions on Cybernetics.

[15]  P. Shi,et al.  Robust adaptive sliding mode control for uncertain delta operator systems , 2009 .

[16]  Shaocheng Tong,et al.  A Combined Backstepping and Stochastic Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control , 2013, IEEE Transactions on Fuzzy Systems.

[17]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[18]  Jaime A. Moreno,et al.  A Lyapunov approach to second-order sliding mode controllers and observers , 2008, 2008 47th IEEE Conference on Decision and Control.

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

[20]  Christopher Edwards,et al.  Adaptive continuous higher order sliding mode control , 2016, Autom..

[21]  Gang Feng,et al.  Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems , 2012, Autom..

[22]  Hak-Keung Lam,et al.  Observer-Based Fuzzy Control for Nonlinear Networked Systems Under Unmeasurable Premise Variables , 2016, IEEE Transactions on Fuzzy Systems.

[23]  Xinping Guan,et al.  Adaptive backstepping control for a class of time delay systems with nonlinear perturbations , 2008 .

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

[25]  Yi Huang,et al.  ADRC With Adaptive Extended State Observer and its Application to Air–Fuel Ratio Control in Gasoline Engines , 2015, IEEE Transactions on Industrial Electronics.

[26]  Jaime A. Moreno,et al.  Adaptive output feedback second order sliding mode control with unknown bound of perturbation , 2014 .

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

[28]  Lihua Xie,et al.  Robust track‐following control of hard disk drives using improved integral sliding mode combined with phase lead peak filter , 2008 .

[29]  Swaroop Darbha,et al.  Dynamic surface control for a class of nonlinear systems , 2000, IEEE Trans. Autom. Control..

[30]  Yuanqing Xia,et al.  Sliding-Mode Predictive Control of Networked Control Systems Under a Multiple-Packet Transmission Policy , 2014, IEEE Transactions on Industrial Electronics.

[31]  Ligang Wu,et al.  Filtering of Interval Type-2 Fuzzy Systems With Intermittent Measurements , 2016, IEEE Transactions on Cybernetics.

[32]  Hak-Keung Lam,et al.  Observer-Based Fault Detection for Nonlinear Systems With Sensor Fault and Limited Communication Capacity , 2016, IEEE Transactions on Automatic Control.

[33]  Bing Chen,et al.  Adaptive neural tracking control of nonlinear time‐delay systems with disturbances , 2009 .

[34]  Leonid M. Fridman,et al.  Continuous terminal sliding-mode controller , 2016, Autom..