Fuzzy adaptive control of nonlinear uncertain plants with unknown dead zone output

This paper focuses on a tracking problem for a class of strict-feedback nonlinear systems with unknown dead-zone output and unmeasurable states. Based on the adaptive backstepping technique, a new adaptive fuzzy control scheme is proposed. It is shown that the proposed control scheme guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, the tracking error converges to a small neighborhood of the origin. Moreover, the proposed control method requires only one adaptive law for an nth-order system and the structure of the controllers is very simple, so they are easy to be implemented. The main advantage of this paper is that the unknown dead-zone nonlinearity in the output mechanism of strict-feedback systems is considered. By introducing a Nussbaum function, the problem of unknown virtual control coefficient is resolved, which is caused by the nonlinearity in the output mechanism. Finally, simulation results are provided to show the effectiveness of the proposed approach.

[1]  Xin-Ping Guan,et al.  Adaptive Tracking Controller Design of Nonlinear Systems With Time Delays and Unknown Dead-Zone Input , 2008, IEEE Transactions on Automatic Control.

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

[3]  Guomin Li,et al.  Robust nonlinear nominal-model following control to overcome deadzone nonlinearities , 2001, IEEE Trans. Ind. Electron..

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

[5]  Gang Tao,et al.  Adaptive Control of Plants with Unknown Dead-zones , 1992, 1992 American Control Conference.

[6]  Chen Bin,et al.  Fuzzy adaptive output feedback control for MIMO nonlinear systems , 2005, Fuzzy Sets Syst..

[7]  Xinping Guan,et al.  Brief paper: adaptive backstepping fault-tolerant control for unmatched non-linear systems against actuator dead-zone , 2010 .

[8]  Licheng Jiao,et al.  Adaptive Backstepping Fuzzy Control for Nonlinearly Parameterized Systems With Periodic Disturbances , 2010, IEEE Transactions on Fuzzy Systems.

[9]  M. MendelJ.,et al.  Fuzzy basis functions , 1995 .

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

[11]  S. Tong,et al.  Observer-based adaptive fuzzy backstepping dynamic surface control for a class of non-linear systems with unknown time delays , 2011 .

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

[13]  Qing Zhu,et al.  Adaptive Fuzzy Control of Nonlinear Systems in Pure Feedback Form Based on Input-to-State Stability , 2010, IEEE Transactions on Fuzzy Systems.

[14]  Gang Tao,et al.  Adaptive Control of Systems with Actuator and Sensor Nonlinearities , 1996 .

[15]  Shaocheng Tong,et al.  Robust Adaptive Tracking Control for Nonlinear Systems Based on Bounds of Fuzzy Approximation Parameters , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[16]  Licheng Jiao,et al.  Adaptive Tracking for Periodically Time-Varying and Nonlinearly Parameterized Systems Using Multilayer Neural Networks , 2010, IEEE Transactions on Neural Networks.

[17]  Petar V. Kokotovic,et al.  Adaptive control of systems with unknown output backlash , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[18]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems with unknown dead-zone , 2004, Autom..

[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]  T. Apostol.  Mathematical Analysis , 1957 .

[21]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Control of MIMO Nonlinear Systems With Unknown Dead-Zone Inputs , 2013, IEEE Transactions on Fuzzy Systems.

[22]  Frank L. Lewis,et al.  Deadzone compensation in motion control systems using neural networks , 2000, IEEE Trans. Autom. Control..

[23]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Tracking Backstepping Control of Strict-Feedback Nonlinear Systems With Unknown Dead Zones , 2012, IEEE Transactions on Fuzzy Systems.

[24]  Shengyuan Xu,et al.  Adaptive Output-Feedback Fuzzy Tracking Control for a Class of Nonlinear Systems , 2011, IEEE Transactions on Fuzzy Systems.

[25]  Bing Chen,et al.  Direct adaptive neural control for strict-feedback stochastic nonlinear systems , 2011, Nonlinear Dynamics.

[26]  Torbjörn Wigren,et al.  Compensation of the RLS algorithm for output nonlinearities , 1999, IEEE Trans. Autom. Control..

[27]  Shaocheng Tong,et al.  A DSC Approach to Robust Adaptive NN Tracking Control for Strict-Feedback Nonlinear Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Shaocheng Tong,et al.  Fuzzy-Adaptive Decentralized Output-Feedback Control for Large-Scale Nonlinear Systems With Dynamical Uncertainties , 2010, IEEE Transactions on Fuzzy Systems.

[29]  Weisheng Chen,et al.  Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign , 2010, Fuzzy Sets Syst..

[30]  Gang Tao,et al.  Adaptive control of system with unknown output backlash , 1995 .

[31]  S. Ge,et al.  Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[32]  Bing Chen,et al.  Adaptive neural tracking control for a class of stochastic nonlinear systems , 2014 .

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

[34]  Ying Zhang,et al.  Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity , 2006, IEEE Transactions on Automatic Control.

[35]  Tong Shao-cheng,et al.  Fuzzy adaptive observer backstepping control for MIMO nonlinear systems , 2009 .

[36]  Maria Letizia Corradini,et al.  Robust practical stabilization of nonlinear uncertain plants with input and output nonsmooth nonlinearities , 2003, IEEE Trans. Control. Syst. Technol..

[37]  Shaocheng Tong,et al.  Observer-based fuzzy adaptive control for strict-feedback nonlinear systems , 2009, Fuzzy Sets Syst..

[38]  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).

[39]  R. Nussbaum.  Some remarks on a conjecture in parameter adaptive control , 1983 .