Adaptive fuzzy finite-time stability of uncertain nonlinear systems based on prescribed performance

Abstract The semi-globally practical finite-time stability (SGPFS) problem for a class of uncertain strict-feedback nonlinear systems is discussed in this paper. A novel performance function called finite-time performance function (FTPF) is first defined. Moreover, this paper is the first to solve an adaptive semi-globally practical finite-time control issue by combining with backstepping, prescribed performance control (PPC) and fuzzy logic systems. Furthermore, it is proven that the designed control law not only guarantees that all the states converge to a predefined zone in finite-time, but also all the signals of the closed-loop systems are SGPF-stable. Simulation examples are worked out to illustrate the superiority and feasibility of the proposed design method.

[1]  Shaocheng Tong,et al.  Adaptive Fuzzy Tracking Control Design for SISO Uncertain Nonstrict Feedback Nonlinear Systems , 2016, IEEE Transactions on Fuzzy Systems.

[2]  Guang-Hong Yang,et al.  Prescribed Performance Fault-Tolerant Control of Uncertain Nonlinear Systems With Unknown Control Directions , 2017, IEEE Transactions on Automatic Control.

[3]  Eugene P. Ryan,et al.  Funnel Control With Saturation: Nonlinear SISO Systems $ $ , 2010, IEEE Transactions on Automatic Control.

[4]  Ting Li,et al.  A new approach to fast global finite-time stabilization of high-order nonlinear system , 2017, Autom..

[5]  Feifei Yang,et al.  Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems with hysteresis input , 2017, Neurocomputing.

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

[7]  Xiaoping Liu,et al.  Direct adaptive fuzzy control of nonlinear strict-feedback systems , 2009, Autom..

[8]  Jang-Myung Lee,et al.  Improved prescribed performance constraint control for a strict feedback non-linear dynamic system , 2013 .

[9]  Ding Zhai,et al.  Prescribed Performance Switched Adaptive Dynamic Surface Control of Switched Nonlinear Systems With Average Dwell Time , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[10]  Chunjiang Qian,et al.  Global finite-time stabilization of a class of upper-triangular systems , 2010, Proceedings of the 2010 American Control Conference.

[11]  Yang Liu,et al.  Adaptive backstepping H∞ tracking control with prescribed performance for internet congestion. , 2017, ISA transactions.

[12]  Xiaofeng Zhang,et al.  Research on Stability Improvement of the Cascaded DC–DC Converters Based on AC Signal Sampling Control Method , 2018, IEEE Transactions on Power Electronics.

[13]  Shihua Li,et al.  Attitude Synchronization for Flexible Spacecraft With Communication Delays , 2016, IEEE Transactions on Automatic Control.

[14]  Shaocheng Tong,et al.  Fuzzy Adaptive Output Feedback Control of MIMO Nonlinear Systems With Partial Tracking Errors Constrained , 2015, IEEE Transactions on Fuzzy Systems.

[15]  Xinzhi Liu,et al.  A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems , 2017, Fuzzy Sets Syst..

[16]  Caoyang Yu,et al.  Adaptive Fuzzy Trajectory Tracking Control of an Under-Actuated Autonomous Underwater Vehicle Subject to Actuator Saturation , 2018, Int. J. Fuzzy Syst..

[17]  Jinde Cao,et al.  Finite-time non-fragile passivity control for neural networks with time-varying delay , 2017, Appl. Math. Comput..

[18]  Shuzhi Sam Ge,et al.  Adaptive Fuzzy Control of a Class of Nonlinear Systems by Fuzzy Approximation Approach , 2012, IEEE Transactions on Fuzzy Systems.

[19]  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.

[20]  Yigang He,et al.  Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  Charalampos P. Bechlioulis,et al.  Robust Adaptive Control of Feedback Linearizable MIMO Nonlinear Systems With Prescribed Performance , 2008, IEEE Transactions on Automatic Control.

[22]  Guang-Hong Yang,et al.  Decentralized Adaptive Fuzzy Secure Control for Nonlinear Uncertain Interconnected Systems Against Intermittent DoS Attacks , 2019, IEEE Transactions on Cybernetics.

[23]  Haixia Wang,et al.  Exponential input-to-state stability for complex-valued memristor-based BAM neural networks with multiple time-varying delays , 2018, Neurocomputing.

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

[25]  Min Wang,et al.  Dynamic Learning From Adaptive Neural Control of Robot Manipulators With Prescribed Performance , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[26]  Frank L. Lewis,et al.  Neuro-adaptive cooperative tracking control with prescribed performance of unknown higher-order nonlinear multi-agent systems , 2018, Int. J. Control.

[27]  Jinde Cao,et al.  Finite-time stabilisation for discrete-time T–S fuzzy model system with channel fading and two types of parametric uncertainty , 2017, Int. J. Syst. Sci..

[28]  Shaocheng Tong,et al.  Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Chong Lin,et al.  Finite-Time Adaptive Fuzzy Tracking Control Design for Nonlinear Systems , 2018, IEEE Transactions on Fuzzy Systems.

[30]  Xiaoping Liu,et al.  Approximation-Based Adaptive Fuzzy Tracking Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Time-Delay Systems , 2015, IEEE Transactions on Fuzzy Systems.

[31]  Yongduan Song,et al.  Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time , 2017, Autom..

[32]  Yongming Li,et al.  Adaptive output-feedback control design with prescribed performance for switched nonlinear systems , 2017, Autom..

[33]  G. Rovithakis,et al.  Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances , 2008, 2008 16th Mediterranean Conference on Control and Automation.

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

[35]  Jinde Cao,et al.  Robust finite-time non-fragile sampled-data control for T-S fuzzy flexible spacecraft model with stochastic actuator faults , 2018, Appl. Math. Comput..

[36]  Chong Lin,et al.  Adaptive finite-time control for a class of uncertain high-order non-linear systems based on fuzzy approximation , 2017 .

[37]  Bing Chen,et al.  Adaptive Neural Tracking Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Systems With Unknown Backlash-Like Hysteresis , 2014, IEEE Transactions on Neural Networks and Learning Systems.

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

[39]  Yuehua Huang,et al.  Global finite-time stabilisation for a class of nonlinear systems , 2012, Int. J. Syst. Sci..

[40]  Yigang He,et al.  Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters , 2014 .

[41]  Shaocheng Tong,et al.  Observed-Based Adaptive Fuzzy Decentralized Tracking Control for Switched Uncertain Nonlinear Large-Scale Systems With Dead Zones , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[42]  Xin-Ping Guan,et al.  Output Feedback Stabilization for Time-Delay Nonlinear Interconnected Systems Using Neural Networks , 2008, IEEE Transactions on Neural Networks.

[43]  Renquan Lu,et al.  Prescribed Performance Observer-Based Adaptive Fuzzy Control for Nonstrict-Feedback Stochastic Nonlinear Systems , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[44]  Salim Labiod,et al.  Adaptive fuzzy control of a class of MIMO nonlinear systems , 2005, Fuzzy Sets Syst..

[45]  Yungang Liu,et al.  Prescribed-Performance Control Design for Pure-Feedback Nonlinear Systems with Most Severe Uncertainties , 2018, SIAM J. Control. Optim..

[46]  Keng Peng Tee,et al.  Adaptive Neural Control for Output Feedback Nonlinear Systems Using a Barrier Lyapunov Function , 2010, IEEE Transactions on Neural Networks.

[47]  Charalampos P. Bechlioulis,et al.  Decentralized Robust Synchronization of Unknown High Order Nonlinear Multi-Agent Systems With Prescribed Transient and Steady State Performance , 2017, IEEE Transactions on Automatic Control.

[48]  Yiguang Hong,et al.  Finite-time stabilization and stabilizability of a class of controllable systems , 2002, Syst. Control. Lett..

[49]  Xiaohua Xia,et al.  Global finite-time observers for a class of nonlinear systems , 2013, Kybernetika.

[50]  Yigang He,et al.  Distributed Finite-Time Cooperative Control of Multiple High-Order Nonholonomic Mobile Robots , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[51]  Bing Chen,et al.  Finite-Time Adaptive Control for a Class of Nonlinear Systems With Nonstrict Feedback Structure , 2018, IEEE Transactions on Cybernetics.

[52]  Jinde Cao,et al.  Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay , 2017, Advances in difference equations.

[53]  Shaocheng Tong,et al.  Adaptive Fuzzy Control With Prescribed Performance for Block-Triangular-Structured Nonlinear Systems , 2018, IEEE Transactions on Fuzzy Systems.

[54]  Zhong-Ping Jiang,et al.  Finite-Time Input-To-State Stability and Applications to Finite-Time Control , 2008 .