Adaptive Tracking Control for a Class of Uncertain Non-affine Delayed Systems Subjected to Input Constraints Using Self Recurrent Wavelet Neural Network

In this work an adaptive tracking control strategy for a class of non affine delayed systems subjected to actuator saturation is proposed. Self recurrent wavelet neural network (SRWNN) is used to approximate the uncertainties present in the system as well as to identify and compensate the nonlinearities introduced in the system due to actuator saturation. By using suitable transformation the system under consideration is first converted into an affine like form and subsequently an adaptive backstepping control strategy is developed to assure the stable tracking of nonlinear non affine system. In addition robust control terms are also designed to attenuate the approximation error due to SRWNN. Adaptation laws are developed for the online tuning of the wavelet parameters and the stability of the overall system is assured by using the Lyapunov-Krasovskii functional. The effectiveness of theoretical development is verified by a numerical example.

[1]  E. Lavretsky,et al.  Dynamic inversion of multi-input nonaffine systems via time-scale separation , 2006, 2006 American Control Conference.

[2]  Sung Jin Yoo,et al.  Stable Predictive Control of Chaotic Systems Using Self-Recurrent Wavelet Neural Network , 2005 .

[3]  Rong-Jong Wai,et al.  Backstepping wavelet neural network control for indirect field-oriented induction motor drive , 2004, IEEE Trans. Neural Networks.

[4]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[5]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[6]  Luca Zaccarian,et al.  Nonlinear antiwindup applied to Euler-Lagrange systems , 2004, IEEE Transactions on Robotics and Automation.

[7]  M. Moraud.  Wavelet Networks , 2018, Foundations of Wavelet Networks and Applications.

[8]  N. Hovakimyan,et al.  Control of a nonaffine double-pendulum system via dynamic inversion and time-scale separation , 2006, 2006 American Control Conference.

[9]  Chih-Min Lin,et al.  Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems , 2006, IEEE Transactions on Neural Networks.

[10]  Jun Zhang,et al.  Wavelet neural networks for function learning , 1995, IEEE Trans. Signal Process..

[11]  Jang-Hyun Park,et al.  Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks , 2005, IEEE Transactions on Neural Networks.

[12]  Jing Zhou,et al.  Adaptive Neural Network Control of Uncertain Nonlinear Systems in the Presence of Input Saturation , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[13]  Jin Bae Park,et al.  Direct adaptive control using self recurrent wavelet neural network via adaptive learning rates for stable path tracking of mobile robots , 2005, Proceedings of the 2005, American Control Conference, 2005..

[14]  Qinghua Zhang,et al.  Wavelet networks , 1992, IEEE Trans. Neural Networks.

[15]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems , 2003, Autom..

[16]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[17]  Ching-Hung Lee,et al.  Direct Adaptive Backstepping Control for a Class of MIMO Non-affine Systems Using Recurrent Neural Networks , 2009 .

[18]  A.J. Calise,et al.  Adaptive Control of a Class of Non-Affine Systems using Neural Networks , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[19]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..