Adaptive fuzzy control for pure-feedback systems with full state constraints and unknown nonlinear dead zone

Abstract In this paper, an adaptive control problem for a class of pure-feedback time-varying delay nonlinear systems with full state constraints and unknown dead zone is investigated. Differing from the full state constraints without considering the time-varying delay in nonlinear systems, a well defined Barrier Lyapunov-Krasovskii functional is designed to address the difficult in this paper. By defining a continuous function and combining with mean value theorem, system is modeled with dead zone. Furthermore, a novel adaptive control scheme is developed based on recursive backstepping method. It is proved that the proposed approach can guarantee a desired tracking performance and semi-global asymptotically stability of the closed-loop system. Finally, some simulation results are given to verify the effectiveness of the proposed strategy.

[1]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[2]  Marios M. Polycarpou,et al.  Stable adaptive neural control scheme for nonlinear systems , 1996, IEEE Trans. Autom. Control..

[3]  Magdi S. Mahmoud,et al.  Feedback fuzzy control for quantized networked systems with random delays , 2016, Appl. Math. Comput..

[4]  Shaocheng Tong,et al.  Adaptive Controller Design-Based ABLF for a Class of Nonlinear Time-Varying State Constraint Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[5]  Fu-Chuang Chen,et al.  Adaptive control of nonlinear systems using neural networks , 1992 .

[6]  Fangfei Li,et al.  On stabilization and set stabilization of multivalued logical systems , 2017, Autom..

[7]  Peng Shi,et al.  Finite-time command filtered backstepping control for a class of nonlinear systems , 2018, Autom..

[8]  Derong Liu,et al.  Residential energy scheduling for variable weather solar energy based on adaptive dynamic programming , 2018, IEEE/CAA Journal of Automatica Sinica.

[9]  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).

[10]  Ju H. Park,et al.  Further Results on Stabilization of Chaotic Systems Based on Fuzzy Memory Sampled-Data Control , 2018, IEEE Transactions on Fuzzy Systems.

[11]  Shuzhi Sam Ge,et al.  Approximation-Based Adaptive Tracking Control of Pure-Feedback Nonlinear Systems With Multiple Unknown Time-Varying Delays , 2010, IEEE Trans. Neural Networks.

[12]  Taeyoung Lee,et al.  Stability of time-delay systems , 1981 .

[13]  Jinkun Liu,et al.  An adaptive RBF neural network control method for a class of nonlinear systems , 2018, IEEE/CAA Journal of Automatica Sinica.

[14]  Yang Yi,et al.  Adaptive Neural Dynamic Surface Control of Pure-Feedback Nonlinear Systems With Full State Constraints and Dynamic Uncertainties , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[15]  Hao Shen,et al.  Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links , 2017, IEEE Transactions on Neural Networks and Learning Systems.

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

[17]  Chun-Yi Su,et al.  Adaptive tracking of nonlinear systems with non-symmetric dead-zone input , 2007, Autom..

[18]  Shaocheng Tong,et al.  A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control , 2009, IEEE Transactions on Fuzzy Systems.

[19]  Cheng-Wu Chen,et al.  Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method , 2008, Appl. Math. Comput..

[20]  Hansheng Wu,et al.  Adaptive stabilizing state feedback controllers of uncertain dynamical systems with multiple time delays , 2000, IEEE Trans. Autom. Control..

[21]  Bing Chen,et al.  Novel adaptive neural control design for nonlinear MIMO time-delay systems , 2009, Autom..

[22]  Shuzhi Sam Ge,et al.  Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs , 2007, Autom..

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

[24]  Junmin Li,et al.  Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays , 2015, Appl. Math. Comput..

[25]  Shaocheng Tong,et al.  Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints , 2016, Autom..

[26]  Feifei Yang,et al.  Adaptive neural tracking control for nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints , 2017, Int. J. Syst. Sci..

[27]  Keng Peng Tee,et al.  Adaptive Control of Electrostatic Microactuators With Bidirectional Drive , 2009, IEEE Transactions on Control Systems Technology.

[28]  Hongjing Liang,et al.  Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints , 2018, Appl. Math. Comput..

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

[30]  Francis Eng Hock Tay,et al.  Barrier Lyapunov Functions for the control of output-constrained nonlinear systems , 2009, Autom..

[31]  Bing Chen,et al.  Adaptive Neural Control for a Class of Perturbed Strict-Feedback Nonlinear Time-Delay Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[32]  Bing Chen,et al.  Fuzzy Approximation-Based Adaptive Control of Nonlinear Delayed Systems With Unknown Dead Zone , 2014, IEEE Transactions on Fuzzy Systems.

[33]  Keng Peng Tee,et al.  Control of nonlinear systems with partial state constraints using a barrier Lyapunov function , 2011, Int. J. Control.

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

[35]  Shengyuan Xu,et al.  Relaxed conditions for stability of time-varying delay systems , 2017, Autom..

[36]  Shaocheng Tong,et al.  Approximation-Based Adaptive Neural Tracking Control of Nonlinear MIMO Unknown Time-Varying Delay Systems With Full State Constraints , 2017, IEEE Transactions on Cybernetics.

[37]  Shuzhi Sam Ge,et al.  Adaptive neural network control of nonlinear systems with unknown time delays , 2003, IEEE Trans. Autom. Control..

[38]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: the smooth feedback case , 2002, IEEE Trans. Autom. Control..

[39]  Bing Chen,et al.  Observer and Adaptive Fuzzy Control Design for Nonlinear Strict-Feedback Systems With Unknown Virtual Control Coefficients , 2018, IEEE Transactions on Fuzzy Systems.

[40]  Youan Zhang,et al.  An exploration on adaptive iterative learning control for a class of commensurate high-order uncertain nonlinear fractional order systems , 2018, IEEE/CAA Journal of Automatica Sinica.

[41]  Keng Peng Tee,et al.  Approximation-based control of nonlinear MIMO time-delay systems , 2007, Autom..

[42]  J. Wang,et al.  Robust adaptive neural control for a class of uncertain non-linear time-delay systems with unknown dead-zone non-linearity , 2011 .

[43]  Ju H. Park,et al.  Event-Based Reliable Dissipative Filtering for T–S Fuzzy Systems With Asynchronous Constraints , 2018, IEEE Transactions on Fuzzy Systems.