High Order Sliding Mode Backstepping Control for a Class of Unknown Pure Feedback Nonlinear Systems

This paper aims at addressing the problem of finite time exact tracking control for a class of unknown nonlinear systems in pure feedback form while guaranteeing the closed-loop stability. The uncertain nonlinear system considered in this paper is not only in completely non-affine form but also explicitly dependent on the time and therefore, can cover a general class of nonlinear systems. By incorporating high order sliding mode controller into backstepping design procedure, a new robust control scheme with novel integrators is proposed, which is able to steer the tracking error to zero. Moreover, the closed loop stability can be proved with the help of the constructed integrators in every design step. Two simulation examples are presented to illustrate the correctness and effectiveness of the proposed control scheme.

[1]  Shuzhi Sam Ge,et al.  Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form , 2008, Autom..

[2]  Jorge Davila,et al.  Exact Tracking Using Backstepping Control Design and High-Order Sliding Modes , 2013, IEEE Transactions on Automatic Control.

[3]  Guang-Hong Yang,et al.  Robust Adaptive Fault-Tolerant Control for a Class of Unknown Nonlinear Systems , 2017, IEEE Transactions on Industrial Electronics.

[4]  Leonid M. Fridman,et al.  Integral HOSM Semiglobal Controller for Finite-Time Exact Compensation of Unmatched Perturbations , 2010, IEEE Transactions on Automatic Control.

[5]  Naser Pariz,et al.  Distributed finite-time control for arbitrary switched nonlinear multi-agent systems: an observer-based approach , 2018 .

[6]  Shaocheng Tong,et al.  Neural Controller Design-Based Adaptive Control for Nonlinear MIMO Systems With Unknown Hysteresis Inputs , 2016, IEEE Transactions on Cybernetics.

[7]  Peng Shi,et al.  Observer and Command-Filter-Based Adaptive Fuzzy Output Feedback Control of Uncertain Nonlinear Systems , 2015, IEEE Transactions on Industrial Electronics.

[8]  C. L. Philip Chen,et al.  Adaptive Inversion-Based Fuzzy Compensation Control of Uncertain Pure-Feedback Systems With Asymmetric Actuator Backlash , 2017, IEEE Transactions on Fuzzy Systems.

[9]  Yan Lin,et al.  A robust adaptive dynamic surface control for a class of nonlinear systems with unknown Prandtl–Ishilinskii hysteresis , 2011 .

[10]  Xiaowei Yu,et al.  Adaptive Backstepping Quantized Control for a Class of Nonlinear Systems , 2017, IEEE Transactions on Automatic Control.

[11]  Leonid Fridman,et al.  Combined backstepping and HOSM control design for a class of nonlinear MIMO systems , 2017 .

[12]  Gang Chen,et al.  Distributed output‐feedback finite‐time tracking control of nonaffine nonlinear leader‐follower multiagent systems , 2020, International Journal of Robust and Nonlinear Control.

[13]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Dynamic Surface Control of Interconnected Nonlinear Pure-Feedback Systems , 2015, IEEE Transactions on Cybernetics.

[14]  Jang-Hyun Park,et al.  Output-Feedback Adaptive Neural Controller for Uncertain Pure-Feedback Nonlinear Systems Using a High-Order Sliding Mode Observer , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Arie Levant,et al.  Quasi-continuous high-order sliding-mode controllers , 2005, IEEE Transactions on Automatic Control.

[16]  Yan Lin,et al.  Adaptive dynamic surface control for pure‐feedback systems , 2012 .

[17]  Qiang Chen,et al.  Adaptive echo state network control for a class of pure-feedback systems with input and output constraints , 2018, Neurocomputing.

[18]  Yongduan Song,et al.  Fraction Dynamic-Surface-Based Neuroadaptive Finite-Time Containment Control of Multiagent Systems in Nonaffine Pure-Feedback Form , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Zhengrong Xiang,et al.  Adaptive practical finite-time stabilization for switched nonlinear systems in pure-feedback form , 2017, J. Frankl. Inst..

[20]  Shuzhi Sam Ge,et al.  An ISS-modular approach for adaptive neural control of pure-feedback systems , 2006, Autom..

[21]  Shengyuan Xu,et al.  Observer-based tracking control for MIMO pure-feedback nonlinear systems with time-delay and input quantisation , 2017, Int. J. Control.

[22]  Jianyong Yao,et al.  Adaptive RISE Control of Hydraulic Systems With Multilayer Neural-Networks , 2019, IEEE Transactions on Industrial Electronics.

[23]  Ning Wang,et al.  Finite-Time Fault Estimator Based Fault-Tolerance Control for a Surface Vehicle With Input Saturations , 2020, IEEE Transactions on Industrial Informatics.

[24]  Sheng-Li Shi,et al.  Extended-State-Observer-Based Chattering Free Sliding Mode Control for Nonlinear Systems With Mismatched Disturbance , 2018, IEEE Access.

[25]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[26]  Yan Lin,et al.  Adaptive Actuator Failure Compensation for a Class of Nonlinear Systems With Unknown Control Direction , 2017, IEEE Transactions on Automatic Control.

[27]  Dan Wang,et al.  Neural network‐based adaptive dynamic surface control of uncertain nonlinear pure‐feedback systems , 2011 .

[28]  Yue Wang,et al.  Adaptive Estimated Inverse Output-Feedback Quantized Control for Piezoelectric Positioning Stage , 2019, IEEE Transactions on Cybernetics.

[29]  Yan Lin,et al.  Adaptive tracking control for a class of pure-feedback non-linear systems including actuator hysteresis and dynamic uncertainties , 2011 .

[30]  Shinji Hokamoto,et al.  Chattering Attenuation Sliding Mode Approach for Nonlinear Systems , 2017 .

[31]  Zongxia Jiao,et al.  RISE-Based Adaptive Control of Hydraulic Systems With Asymptotic Tracking , 2017, IEEE Transactions on Automation Science and Engineering.

[32]  Hongkun He,et al.  Dynamics-Level Finite-Time Fuzzy Monocular Visual Servo of an Unmanned Surface Vehicle , 2020, IEEE Transactions on Industrial Electronics.

[33]  Keng Peng Tee,et al.  Adaptive NN control for uncertain pure-feedback nonlinear systems with state constraints subject to unknown disturbances , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).