Adaptive control of uncertain non-affine pure feedback nonlinear systems using backstepping techniques

In this paper, a robust adaptive control law for a class of uncertain non-affine nonlinear systems is proposed. The proposed controller guarantees asymptotic output tracking of systems in the pure feedback form with unknown static parameters and non- affine controller. This controller takes advantages of a robust stability property of the Lyapunov redesign method and a systematic design procedure of the backstepping technique. Using the Lyapunov redesign method in each step of the conventional backstepping technique makes backstepping robust. The suggested controller is designed through repeatedly utilizing the Lyapunov redesign method in each step of the backstepping technique and derivative of the controller. Simulation results reveal the efficiency of the Lyapunov redesign-based backstepping controller.

[1]  Xin-Ping Guan,et al.  Robust controller design for uncertain multiple-delay systems with unknown actuator parameters , 2012, Autom..

[2]  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..

[3]  Delay‐dependent asymptotic stability of BAM neural networks with time delay , 2010 .

[4]  Isaac Chairez Oria,et al.  Nonlinear discrete time neural network observer , 2013, Neurocomputing.

[5]  Xin Yang,et al.  New delay-variation-dependent stability for neural networks with time-varying delay , 2013, Neurocomputing.

[6]  Quan Min Zhu,et al.  A Correlation-Test-Based Validation Procedure for Identified Neural Networks , 2009, IEEE Transactions on Neural Networks.

[7]  Shan Liu,et al.  Development of a new EDRNN procedure in control of human arm trajectories , 2008, Neurocomputing.

[8]  Shuzhi Sam Ge,et al.  Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems , 2003, Autom..

[9]  Dan Wang,et al.  Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form , 2002, Autom..

[10]  Yang Li,et al.  A generalized indirect adaptive neural networks backstepping control procedure for a class of non-affine nonlinear systems with pure-feedback prototype , 2013, Neurocomputing.

[11]  Tao Zhang,et al.  Design and performance analysis of a direct adaptive controller for nonlinear systems , 1999, Autom..

[12]  Wen Yu,et al.  Nonlinear system identification with recurrent neural networks and dead-zone Kalman filter algorithm , 2007, Neurocomputing.

[13]  Xin-Ping Guan,et al.  Stability of Cellular Neural Networks with Time Varying Delay , 2010, 2008 Fourth International Conference on Natural Computation.

[14]  Wen Yu,et al.  Stability Analysis of Nonlinear System Identification via Delayed Neural Networks , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.