A novel neural approximate inverse control for unknown nonlinear discrete dynamical systems

A novel neural approximate inverse control is proposed for general unknown single-input-single-output (SISO) and multi-input-multi-output (MIMO) nonlinear discrete dynamical systems. Based on an innovative input/output (I/O) approximation of neural network nonlinear models, the neural inverse control law can be derived directly and its implementation for an unknown process is straightforward. Only a general identification technique is involved in both model development and control design without extra training (online or offline) for the neural nonlinear inverse controller. With less approximation made on controller development, the control will be more robust to large variations in the operating region. The robustness of the stability and the performance of a closed-loop system can be rigorously established even if the nonlinear plant is of not well defined relative degree. Extensive simulations demonstrate the performance of the proposed neural inverse control.

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

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

[3]  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..

[4]  Vincenzo Piuri,et al.  A neural-network based control solution to air-fuel ratio control for automotive fuel-injection systems , 2003, IEEE Trans. Syst. Man Cybern. Part C.

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

[6]  Dale E. Seborg,et al.  Nonlinear internal model control strategy for neural network models , 1992 .

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

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

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

[10]  Sylvie Galichet,et al.  Nonlinear internal model control: application of inverse model based fuzzy control , 2003, IEEE Trans. Fuzzy Syst..

[11]  Bernard Widrow,et al.  Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

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

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

[14]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

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

[16]  B. Widrow,et al.  Adaptive inverse control , 1987, Proceedings of 8th IEEE International Symposium on Intelligent Control.

[17]  Léon Personnaz,et al.  Nonlinear internal model control using neural networks: application to processes with delay and design issues , 2000, IEEE Trans. Neural Networks Learn. Syst..

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

[19]  S. Nash,et al.  Linear and Nonlinear Programming , 1987 .

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

[21]  Ju-Yeop Choi,et al.  A constructive approach for nonlinear system identification using multilayer perceptrons , 1996, IEEE Trans. Syst. Man Cybern. Part B.

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

[23]  George W. Irwin,et al.  Nonlinear control structures based on embedded neural system models , 1997, IEEE Trans. Neural Networks.