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Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm
1.  Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China 
2.  Department of Mathematics, Cleveland State University, Cleveland, OH 44115, United States 
References:
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A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence,, IEEE Transcations on Neural Networks, 11 (2000), 697. doi: 10.1109/72.846741. Google Scholar 
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Y. Fang and T. W. S. Chow, Nonlinear dynamical systems control using a new RNN temporal learning strategy,, IEEE Trans on Circuit and Systems, 52 (2005), 719. Google Scholar 
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R. A. Conn, K. Scheinberg and N. L. Vicente, "Introduction to Derivativefree Optimization,", SIAM, (2009). doi: 10.1137/1.9780898718768. Google Scholar 
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J. F. G. Freitas, M. Niranjan, A. H. Gee and A. Doucet, Sequential Monte Carlo methods to train neural network models,, Neural Computation, 12 (2000), 955. doi: 10.1162/089976600300015664. Google Scholar 
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L. K. Li, Learning sunspot series dynamics by recurrent neural networks,, in, (2003), 107. doi: 10.1142/9789812704955_0009. Google Scholar 
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L. K. Li, W. K. Pang, W. T. Yu and M. D. Trout, Forecasting shortterm exchange Rates: a recurrent neural network approach,, in, (2004), 195. doi: 10.4018/9781591401766.ch010. Google Scholar 
[7] 
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations,, International Journal of Pure and Applied Mathematics, 39 (2007), 545. Google Scholar 
[8] 
L. K. Li and S. Shao, A neural network approach for global optimization with applications,, Neural Network World, 18 (2008), 365. Google Scholar 
[9] 
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the shortterm foreign exchange rates,, Applied Mathematical Sciences, 2 (2008), 1705. Google Scholar 
[10] 
X. D. Li, J. K. L. Ho and T. W. S. Chow, Approximation of dynamical timevariant systems by continuoustime recurrent neural networks,, IEEE Trans on Circuit and Systems, 52 (2005), 656. Google Scholar 
[11] 
X. B. Liang and J. Wang, A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints,, IEEE Transactions on Neural Networks, 11 (2000), 1251. doi: 10.1109/72.883412. Google Scholar 
[12] 
Z. Liu and I. Elhanany, A Fast and Scalable Recurrent Neural Network Based on Stochastic Meta Descent,, IEEE Transactions on Neural Networks, 19 (2008), 1652. doi: 10.1109/TNN.2008.2000838. Google Scholar 
[13] 
S. Wang, Q. Shao and X. Zhou, Knotoptimizing spline networks (KOSNETS) for nonparametric regression,, Journal of Industrial and Management Optimization, 4 (2008). Google Scholar 
[14] 
X. Wang and E. K. Blum, Discretetime versus continuoustime models of neural networks,, Journal of Computer and System Sciences, 45 (1992), 1. doi: 10.1016/00220000(92)90038K. Google Scholar 
[15] 
R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks,, Neural Computation, 1 (1989), 270. doi: 10.1162/neco.1989.1.2.270. Google Scholar 
[16] 
L. Xu and W. Liu, A new recurrent neural network adaptive approach for hostgate way rate control protocol within intranets using ATM ABR service,, Journal of Industrial and Management Optimization, 1 (2005), 389. Google Scholar 
[17] 
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex,, Neural Computation, 34 (2000), 79. Google Scholar 
[18] 
K. F. C. Yiu, S. Wang, K. L. Teo and A. H. Tsoi, Nonlinear system modeling via knotoptimizing Bspline networks,, IEEE Transactions on Neural Networks, 12 (2001), 1013. doi: 10.1109/72.950131. Google Scholar 
[19] 
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization,, Journal of Global Optimization, 28 (2004), 229. doi: 10.1023/B:JOGO.0000015313.93974.b0. Google Scholar 
show all references
References:
[1] 
A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence,, IEEE Transcations on Neural Networks, 11 (2000), 697. doi: 10.1109/72.846741. Google Scholar 
[2] 
Y. Fang and T. W. S. Chow, Nonlinear dynamical systems control using a new RNN temporal learning strategy,, IEEE Trans on Circuit and Systems, 52 (2005), 719. Google Scholar 
[3] 
R. A. Conn, K. Scheinberg and N. L. Vicente, "Introduction to Derivativefree Optimization,", SIAM, (2009). doi: 10.1137/1.9780898718768. Google Scholar 
[4] 
J. F. G. Freitas, M. Niranjan, A. H. Gee and A. Doucet, Sequential Monte Carlo methods to train neural network models,, Neural Computation, 12 (2000), 955. doi: 10.1162/089976600300015664. Google Scholar 
[5] 
L. K. Li, Learning sunspot series dynamics by recurrent neural networks,, in, (2003), 107. doi: 10.1142/9789812704955_0009. Google Scholar 
[6] 
L. K. Li, W. K. Pang, W. T. Yu and M. D. Trout, Forecasting shortterm exchange Rates: a recurrent neural network approach,, in, (2004), 195. doi: 10.4018/9781591401766.ch010. Google Scholar 
[7] 
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations,, International Journal of Pure and Applied Mathematics, 39 (2007), 545. Google Scholar 
[8] 
L. K. Li and S. Shao, A neural network approach for global optimization with applications,, Neural Network World, 18 (2008), 365. Google Scholar 
[9] 
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the shortterm foreign exchange rates,, Applied Mathematical Sciences, 2 (2008), 1705. Google Scholar 
[10] 
X. D. Li, J. K. L. Ho and T. W. S. Chow, Approximation of dynamical timevariant systems by continuoustime recurrent neural networks,, IEEE Trans on Circuit and Systems, 52 (2005), 656. Google Scholar 
[11] 
X. B. Liang and J. Wang, A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints,, IEEE Transactions on Neural Networks, 11 (2000), 1251. doi: 10.1109/72.883412. Google Scholar 
[12] 
Z. Liu and I. Elhanany, A Fast and Scalable Recurrent Neural Network Based on Stochastic Meta Descent,, IEEE Transactions on Neural Networks, 19 (2008), 1652. doi: 10.1109/TNN.2008.2000838. Google Scholar 
[13] 
S. Wang, Q. Shao and X. Zhou, Knotoptimizing spline networks (KOSNETS) for nonparametric regression,, Journal of Industrial and Management Optimization, 4 (2008). Google Scholar 
[14] 
X. Wang and E. K. Blum, Discretetime versus continuoustime models of neural networks,, Journal of Computer and System Sciences, 45 (1992), 1. doi: 10.1016/00220000(92)90038K. Google Scholar 
[15] 
R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks,, Neural Computation, 1 (1989), 270. doi: 10.1162/neco.1989.1.2.270. Google Scholar 
[16] 
L. Xu and W. Liu, A new recurrent neural network adaptive approach for hostgate way rate control protocol within intranets using ATM ABR service,, Journal of Industrial and Management Optimization, 1 (2005), 389. Google Scholar 
[17] 
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex,, Neural Computation, 34 (2000), 79. Google Scholar 
[18] 
K. F. C. Yiu, S. Wang, K. L. Teo and A. H. Tsoi, Nonlinear system modeling via knotoptimizing Bspline networks,, IEEE Transactions on Neural Networks, 12 (2001), 1013. doi: 10.1109/72.950131. Google Scholar 
[19] 
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization,, Journal of Global Optimization, 28 (2004), 229. doi: 10.1023/B:JOGO.0000015313.93974.b0. Google Scholar 
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