Feedback-Linearization-Based Neural Adaptive Control for Unknown Nonaffine Nonlinear Discrete-Time Systems

A new feedback-linearization-based neural network (NN) adaptive control is proposed for unknown nonaffine nonlinear discrete-time systems. An equivalent model in afflne-like form is first derived for the original nonaffine discrete-time systems as feedback linearization methods cannot be implemented for such systems. Then, feedback linearization adaptive control is implemented based on the affine-like equivalent model identified with neural networks. Pretraining is not required and the weights of the neural networks used in adaptive control are directly updated online based on the input-output measurement. The dead-zone technique is used to remove the requirement of persistence excitation during the adaptation. With the proposed neural network adaptive control, stability and performance of the closed-loop system are rigorously established. Illustrated examples are provided to validate the theoretical findings.

[1]  C. Harris,et al.  Advanced Adaptive Control , 1995 .

[2]  Madan M. Gupta,et al.  Neuro-Control Systems: Theory and Applications , 1993 .

[3]  Snehasis Mukhopadhyay,et al.  Adaptive control using neural networks and approximate models , 1997, IEEE Trans. Neural Networks.

[4]  O. Nelles.  Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models , 2000 .

[5]  Shuzhi Sam Ge,et al.  Adaptive MNN control for a class of non-affine NARMAX systems with disturbances , 2004, Syst. Control. Lett..

[6]  M. S. Ahmed.  Neural-net-based direct adaptive control for a class of nonlinear plants , 2000, IEEE Trans. Autom. Control..

[7]  Lee H. Keel,et al.  Robust adaptive control of nonaffine nonlinear plants with small input signal changes , 2004, IEEE Transactions on Neural Networks.

[8]  S. S. Ge,et al.  Adaptive NN control for a class of discrete-time non-linear systems , 2003 .

[9]  Anthony J. Calise,et al.  Adaptive Control of a Class of Nonaffine Systems Using Neural Networks , 2007, IEEE Transactions on Neural Networks.

[10]  Daniel G. Sbarbaro-Hofer,et al.  An adaptive sliding-mode controller for discrete nonlinear systems , 2000, IEEE Trans. Ind. Electron..

[11]  Jagannathan Sarangapani,et al.  Neural Network Control of Nonlinear Discrete-Time Systems , 2018 .

[12]  Guanrong Chen,et al.  Spectral-approximation-based intelligent modeling for distributed thermal processes , 2005, IEEE Transactions on Control Systems Technology.

[13]  Liang Jin,et al.  Fast neural learning and control of discrete-time nonlinear systems , 1995, IEEE Trans. Syst. Man Cybern..

[14]  Paul J. Werbos,et al.  Backpropagation Through Time: What It Does and How to Do It , 1990, Proc. IEEE.

[15]  Thomas Parisini,et al.  Active State Estimation for Nonlinear Systems: A Neural Approximation Approach , 2007, IEEE Transactions on Neural Networks.

[16]  Kurt Hornik,et al.  FEED FORWARD NETWORKS ARE UNIVERSAL APPROXIMATORS , 1989 .

[17]  Bernard Mulgrew,et al.  Nonlinear prediction of chaotic signals using a normalised radial basis function network , 2002, Signal Process..

[18]  Sarangapani Jagannathan,et al.  Control of a class of nonlinear discrete-time systems using multilayer neural networks , 2001, IEEE Trans. Neural Networks.

[19]  Dierk Schroder.  Intelligent Observer and Control Design for Nonlinear Systems , 2000 .

[20]  Guido Bugmann,et al.  Normalized Gaussian Radial Basis Function networks , 1998, Neurocomputing.

[21]  Jianming Lu,et al.  Adaptive Control for Nonlinear Systems Using Neural Networks , 1999 .

[22]  Quanmin Zhu,et al.  Stable adaptive neurocontrol for nonlinear discrete-time systems , 2004, IEEE Trans. Neural Networks.

[23]  Han-Xiong Li,et al.  On the new method for the control of discrete nonlinear dynamic systems using neural networks , 2006, IEEE Trans. Neural Networks.

[24]  Snehasis Mukhopadhyay,et al.  Adaptive control of nonlinear multivariable systems using neural networks , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[25]  Kumpati S. Narendra,et al.  Issues in the application of neural networks for tracking based on inverse control , 1999, IEEE Trans. Autom. Control..

[26]  Gregory L. Plett,et al.  Adaptive inverse control of linear and nonlinear systems using dynamic neural networks , 2003, IEEE Trans. Neural Networks.

[27]  Ronald J. Williams,et al.  Experimental Analysis of the Real-time Recurrent Learning Algorithm , 1989 .

[28]  Sangtae Kim,et al.  Linear operator methods in chemical engineering. By D. Ramkrishna and N. Amundson, Prentice-Hall, Englewood Cliffs, NJ, 471 pp., 1985, $51.95 , 1988 .

[29]  Kevin M. Passino,et al.  Stable Adaptive Control and Estimation for Nonlinear Systems , 2001 .

[30]  Hassan K. Khalil,et al.  Adaptive control of a class of nonlinear discrete-time systems using neural networks , 1995, IEEE Trans. Autom. Control..

[31]  Niels Kjølstad Poulsen,et al.  Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner’s Handbook , 2000 .

[32]  Adam Krzyzak,et al.  Nonparametric regression estimation by normalized radial basis function networks , 2003, IEEE Transactions on Information Theory.

[33]  Han-Xiong Li,et al.  An approximate internal model-based neural control for unknown nonlinear discrete processes , 2006, IEEE Transactions on Neural Networks.

[34]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[35]  D. C. Kennedy,et al.  Stabilizing control of a high-order generator model by adaptive feedback linearization , 2003 .

[36]  Nader Sadegh,et al.  A perceptron network for functional identification and control of nonlinear systems , 1993, IEEE Trans. Neural Networks.

[37]  Frank L. Lewis,et al.  Multilayer discrete-time neural-net controller with guaranteed performance , 1996, IEEE Trans. Neural Networks.

[38]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[39]  Lee H. Keel,et al.  A new method for the control of discrete nonlinear dynamic systems using neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[40]  Hong Wang,et al.  A direct adaptive neural-network control for unknown nonlinear systems and its application , 1998, IEEE Trans. Neural Networks.

[41]  J. Sjöberg.  Neural networks for modelling and control of dynamic systems: M. Nørgaard, O. Ravn, N. K. Poulsen and L. K. Hansen. Springer-Verlag, London Berlin Heidelberg, 2000, pp. xiv+246 , 2004 .

[42]  Jie Huang,et al.  Neural-Network-Based Approximate Output Regulation of Discrete-Time Nonlinear Systems , 2007, IEEE Transactions on Neural Networks.

[43]  Han-Xiong Li,et al.  A novel neural approximate inverse control for unknown nonlinear discrete dynamical systems , 2005, IEEE Trans. Syst. Man Cybern. Part B.