Nonlinear System Identification using Neural Networks

This paper proposes a computationally efficient artificial neural network (ANN) model for system identification of unknown dynamic nonlinear discrete time systems. A single layer functional link ANN is used for the model where the need of hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials. Thus, creation of nonlinear decision boundaries in the multidimensional input space and approximation of complex nonlinear systems becomes easier. These models are linear in their parameters and nonlinear in the inputs. The recursive least squares method with forgetting factor is used as on-line learning algorithm for parameter updation. The good behaviour of the identification method is tested on Box and Jenkins Gas furnace benchmark identification problem, single input single output (SISO) and multi input multi output (MIMO) discrete time plants. Stability of the identification scheme is also addressed.

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

[2]  Richard S. Sutton,et al.  Neural networks for control , 1990 .

[3]  CONNECTIONIST LEARNING WITH CHEBYCHEV NETWORKS AND ANALYSES OF ITS INTERNAL REPRESENTATION , 1991 .

[4]  Jean-Jacques E. Slotine,et al.  Stable adaptive control and recursive identification using radial Gaussian networks , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[5]  Stephen A. Billings,et al.  International Journal of Control , 2004 .

[6]  F. L. Lewis,et al.  Identification of a class of nonlinear dynamical systems using multilayer neural networks , 1994, Proceedings of 1994 9th IEEE International Symposium on Intelligent Control.

[7]  Ching-Shiow Tseng,et al.  An orthogonal neural network for function approximation , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[8]  Tsu-Tian Lee,et al.  The Chebyshev-polynomials-based unified model neural networks for function approximation , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Ganapati Panda,et al.  Identification of nonlinear dynamic systems using functional link artificial neural networks , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[10]  Sung-Kwun Oh,et al.  The design of self-organizing Polynomial Neural Networks , 2002, Inf. Sci..

[11]  Alex ChiChung Kot,et al.  Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[12]  Indra Narayan Kar,et al.  On-line system identification using Chebyshev neural networks , 2003, TENCON 2003. Conference on Convergent Technologies for Asia-Pacific Region.

[13]  Emil Levi,et al.  Identification of complex systems based on neural and Takagi-Sugeno fuzzy model , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).