Identification of Nonlinear Systems Using Radial Basis Function Neural Network

This paper uses the radial basis function neural
network (RBFNN) for system identification of nonlinear systems.
Five nonlinear systems are used to examine the activity of RBFNN in
system modeling of nonlinear systems; the five nonlinear systems are
dual tank system, single tank system, DC motor system, and two
academic models. The feed forward method is considered in this
work for modelling the non-linear dynamic models, where the KMeans
clustering algorithm used in this paper to select the centers of
radial basis function network, because it is reliable, offers fast
convergence and can handle large data sets. The least mean square
method is used to adjust the weights to the output layer, and
Euclidean distance method used to measure the width of the Gaussian
function.





References:
[1] S. Haykin, “Neural Networks, A Comprehensive Foundation”, Prentice-
Hall Inc., second edition, USA, 1999.
[2] Bose, and P. Liang, “Neural Network Fundamentals with Graphs,
Algorithms and Applications”, McGraw-Hill series in Electrical and
Computer Engineering, USA, 1996.
[3] Kriesel, “A Brief Introduction to Neural Networks”, Zeta2, University of
Bonn, Germany, 2005.
[4] J. Li, and F. Zhao, “Identification of Dynamical Systems Using Radial
Basis Function Neural Networks with Hybrid Learning Algorithm”,
Systems and Control in Aerospace and Astronautics, ISSCAA 2006.
[5] M. Y. Mashor, “Nonlinear system identification using RBF networks
with linear input connections”, Malaysian Journal of Computer Science,
Vol. 11 No. 1, June 1998, pp. 74-80.
[6] M. Jafari, T. Alizadeh, M. Gholami, A. Alizadeh and K. Salahshoor
“On-line Identification of Non-Linear Systems Using an Adaptive RBFBased
Neural Network”, Proceedings of the World Congress on
Engineering and Computer Science WCECS 2007, San Francisco, USA.
[7] A. Zahir and C. Abdelfettah , “Nonlinear Systems Modelling Using RBF
Neural Networks A Random Learning Approach to the Resource
Allocating Network Algorithm”, Proceedings of the 10th Mediterranean
Conference on Control and Automation - MED2002, Portugal,
[8] M. Wilamowski, “Neural Network Architectures and Learning
Algorithms: How Not to Be Frustrated with Neural Networks”, IEEE
Industrial Electronics Magazine, vol. 3, pp. 56-63, Dec. 2009.
[9] B. M. Wilamowski and H. Yu, “Neural Network Learning without
Backpropagation”, IEEE Trans. On Neural Networks, vol. 21, pp. 1793-
1803, Nov. 2010.
[10] V. Mladenov, P. Koprinkova-Hristova, G. Palm, A. Villa, B. Apolloni,
and K. Kasabov, “Artificial Neural Networks and Machine Learning”,
Springer, USA, 2013.
[11] L. D. Kiernan, J. D. Maso, and K. Warwick, “Robust Initialization of
Gaussian Radial Basis Function Networks Using Partitioned k-means
Clustering”, IEE Electronic Letters, Vol. 32, No. 7, pp.671-673, 1996.
[12] L. Jinkun, “Radial Basis Function (RBF) Neural Network control for
Mechanical Systems”, Springer, USA, 2013.
[13] Y. Hu and J. Hwang, “Hand book of Neural Network Signal
Processing”, by CRC press LLC, USA, 2002.
[14] M. T. Hagan, M. B. Menhaj, “Training Feedforward Networks with the
Marquardt Algorithm”, IEEE Trans. On Neural Networks, vol. 5, no. 6,
pp. 989-993, Nov. 1994.
[15] N. B. Karayiannis, “Reformulated Radial Basis Neural Networks
Trained by Gradient Descent”, IEEE Trans. Neural Networks, vol. 10,
pp. 657-671, Aug. 2002.
[16] J. Fathala, “Analysis and implementation of radial basis function neural
network for controlling non-linear dynamical systems”, PhD. Thesis,
University of Newcastle Upon Tyne, UK. Department of Electrical and
Electronic Engineering, 1998.
[17] J. Moody, and C. Darken, “Fast learning in Networks of Locally-Tuned
Processing Units”, neural computation, Vol. 1, 1989.
[18] R. Mammone, “Artificial Neural Networks for Speech and Vision”, New
Jersey, USA, 1994.
[19] L. Fu, “Neural Networks in Computer Intelligence”, university of
Florida, 1994.
[20] Czarkowski, “Identification and optimization of PID parameters using
Matlab”, Cork institute of technology, Cork, Poland, 2002.
[21] A. Abdulaziz, “Neural Based Controller Development for solving Nonlinear
Control Problem”, PhD. Thesis, University of Newcastle Upon
Tyne, UK, 1994.
[22] T. Phung, and V. Tzouansas, “Design and control of a twin tank water
process”, Engineering department, University of Houston, Downtown,
USA, 2012.
[23] Vasitstha, “PID Output Fuzzified Water Level Control in MIMO
Coupled Tank System", International Journal of Mechanical Engineering
and Technology (IJMET), VOL. 4, PP. 138-153, 2013.
[24] Laubwald, “Coupled tank system 1”, UK, 2014. www.control-systemspriciples.
co.uk (online).
[25] J. Choi, “Control systems, Modelling of DC motors”, university of
British Columbia, Canada, 2008.