Direct Adaptive Fuzzy Tracking Control of Non-affine Stochastic Nonlinear Time-Delay Systems

In this research, the problem of direct adaptive fuzzy control based on state feedback for a class of non-affine stochastic nonlinear systems with time delay is considered. Fuzzy logic systems (FLSs) and mean value theorem are utilized to overcome the design difficulties appeared in the unknown nonlinearities and non-affine structure, respectively. With the utilization of adaptive control and backstepping design framework, a direct adaptive fuzzy control method is developed. Through Lyapunov analysis, the presented controller can guarantee that the variables in the closed-loop system are all bounded in the fourth-moment, in the mean time, the output signal can track the given reference signal by appropriately selecting the design parameters. Simulation results are provided to illustrate the correctness of the theoretical results.

[1]  Yumei Sun,et al.  Finite-Time Fuzzy Control of Stochastic Nonlinear Systems , 2020, IEEE Transactions on Cybernetics.

[2]  Ting Li,et al.  A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems , 2016, Autom..

[3]  Wei Sun,et al.  Command Filter-Based Finite-Time Adaptive Fuzzy Control for Uncertain Nonlinear Systems With Prescribed Performance , 2020, IEEE Transactions on Fuzzy Systems.

[4]  Antonio T. Alexandridis,et al.  NN-Based Adaptive Tracking Control of Uncertain Nonlinear Systems Disturbed by Unknown Covariance Noise , 2007, IEEE Transactions on Neural Networks.

[5]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Meng Joo Er,et al.  Reduced Adaptive Fuzzy Decoupling Control for Lower Limb Exoskeleton , 2020, IEEE Transactions on Cybernetics.

[7]  Shaocheng Tong,et al.  Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics , 2017, IEEE Transactions on Cybernetics.

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

[9]  Krishna R. Pattipati,et al.  A Markov Chain-Based Testability Growth Model With a Cost-Benefit Function , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[10]  H. F. Ho,et al.  Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form. , 2008, ISA transactions.

[11]  Hamid Reza Karimi,et al.  Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays , 2010, IEEE Transactions on Automation Science and Engineering.

[12]  Huanqing Wang,et al.  Adaptive neural control for non-strict-feedback nonlinear systems with input delay , 2020, Inf. Sci..

[13]  Huaguang Zhang,et al.  Neural Observer and Adaptive Neural Control Design for a Class of Nonlinear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Shaocheng Tong,et al.  Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems , 2014, Science China Information Sciences.

[15]  Reza Shahnazi,et al.  Fuzzy Adaptive Tracking Control of Constrained Nonlinear Switched Stochastic Pure-Feedback Systems , 2017, IEEE Transactions on Cybernetics.

[16]  Xue-Jun Xie,et al.  Further Results on Output-Feedback Stabilization for a Class of Stochastic Nonlinear Systems , 2011, IEEE Transactions on Automatic Control.

[17]  Shuzhi Sam Ge,et al.  Robust adaptive control of nonlinear systems with unknown time delays , 2004, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004..

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

[19]  C. L. Philip Chen,et al.  Fuzzy Adaptive Quantized Control for a Class of Stochastic Nonlinear Uncertain Systems , 2016, IEEE Transactions on Cybernetics.

[20]  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.

[21]  T. Apostol Mathematical Analysis , 1957 .

[22]  Zhaoxu Yu,et al.  Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: A Razumikhin functional method , 2011, Neurocomputing.

[23]  Xuehua Li,et al.  Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems , 2017, IEEE Transactions on Cybernetics.

[24]  Huanqing Wang,et al.  Finite-time adaptive fault-tolerant control for nonlinear systems with multiple faults , 2019, IEEE/CAA Journal of Automatica Sinica.

[25]  Xue-Jun Xie,et al.  Adaptive backstepping controller design using stochastic small-gain theorem , 2007, Autom..

[26]  Shaocheng Tong,et al.  Hybrid Fuzzy Adaptive Output Feedback Control Design for Uncertain MIMO Nonlinear Systems With Time-Varying Delays and Input Saturation , 2016, IEEE Transactions on Fuzzy Systems.

[27]  Tieshan Li,et al.  Output-Feedback Adaptive Neural Control for Stochastic Nonlinear Time-Varying Delay Systems With Unknown Control Directions , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[28]  Peng Shi,et al.  Robust backstepping control for a class of time delayed systems , 2005, IEEE Transactions on Automatic Control.

[29]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[30]  Tielong Shen,et al.  Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach , 2005, IEEE Transactions on Automatic Control.

[31]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[32]  C. L. Philip Chen,et al.  Event Trigger Fuzzy Adaptive Compensation Control of Uncertain Stochastic Nonlinear Systems With Actuator Failures , 2018, IEEE Transactions on Fuzzy Systems.

[33]  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.

[34]  Peng Shi,et al.  Quantized Control of Markov Jump Nonlinear Systems Based on Fuzzy Hidden Markov Model , 2019, IEEE Transactions on Cybernetics.

[35]  Licheng Jiao,et al.  Adaptive NN Backstepping Output-Feedback Control for Stochastic Nonlinear Strict-Feedback Systems With Time-Varying Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[36]  Shaocheng Tong,et al.  Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties , 2010, Science China Information Sciences.

[37]  Chong Lin,et al.  Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems. , 2017, IEEE transactions on cybernetics.

[38]  Li Ma,et al.  Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization , 2019, J. Frankl. Inst..

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

[40]  Shengyuan Xu,et al.  Observer-Based Adaptive Neural Network Control for Nonlinear Stochastic Systems With Time Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Zhong-Ping Jiang,et al.  Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems , 2007, Autom..

[42]  Hamid Reza Karimi,et al.  Networked Fault Detection for Markov Jump Nonlinear Systems , 2018, IEEE Transactions on Fuzzy Systems.

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

[44]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..

[45]  S. Ge,et al.  Modeling and Vibration Control for a Nonlinear Moving String With Output Constraint , 2015, IEEE/ASME Transactions on Mechatronics.

[46]  Changyin Sun,et al.  Fuzzy Tracking Control for a Class of Uncertain MIMO Nonlinear Systems With State Constraints , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[47]  Sing Kiong Nguang,et al.  Robust stabilization of a class of time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[48]  C. L. Philip Chen,et al.  Fuzzy Adaptive Compensation Control of Uncertain Stochastic Nonlinear Systems With Actuator Failures and Input Hysteresis , 2019, IEEE Transactions on Cybernetics.

[49]  Shuzhi Sam Ge,et al.  Adaptive NN control of uncertain nonlinear pure-feedback systems , 2002, Autom..

[50]  Weisheng Chen,et al.  Adaptive NN output‐feedback decentralized stabilization for a class of large‐scale stochastic nonlinear strict‐feedback systems , 2011 .

[51]  Peter Xiaoping Liu,et al.  Adaptive Neural Output-Feedback Decentralized Control for Large-Scale Nonlinear Systems With Stochastic Disturbances , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[52]  Peng Shi,et al.  Sliding Mode Control of Singular Stochastic Markov Jump Systems , 2017, IEEE Transactions on Automatic Control.

[53]  Dacheng Tao,et al.  Patch Alignment Manifold Matting , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[54]  M. Krstić,et al.  Stochastic nonlinear stabilization—II: inverse optimality , 1997 .

[55]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Control for a Class of Nonlinear Systems With Full State Constraints , 2018, IEEE Transactions on Fuzzy Systems.

[56]  Yuan JianJiang,et al.  Direct Fuzzy Tracking Control of a Class of Nonaffine Stochastic Nonlinear Systems with Unknown Dead-Zone Input , 2008 .

[57]  Shaocheng Tong,et al.  Adaptive Fuzzy Fault-Tolerant Control of Nontriangular Structure Nonlinear Systems With Error Constraint , 2018, IEEE Transactions on Fuzzy Systems.

[58]  Yue Li,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems. , 2011, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.