Page 101 - Neural Network Modeling and Identification of Dynamical Systems
P. 101
REFERENCES 89
[33] Chen S, Wang SS, Harris C. NARX-based non- [49] Gill PE, Murray W, Wright MH. Practical optimization.
linear system identification using orthogonal least London, New York: Academic Press; 1981.
squares basis hunting. IEEE Trans Control Syst Tech- [50] Nocedal J, Wright S. Numerical optimization. 2nd ed.
nol 2008;16(1):78–84. Springer; 2006.
[34] Sahoo HK, Dash PK, Rath NP. NARX model based [51] Fletcher R. Practical methods of optimization.
nonlinear dynamic system identification using low 2nd ed. New York, NY, USA: Wiley-Interscience.
complexity neural networks and robust H ∞ filter. ISBN 0-471-91547-5, 1987.
Appl Soft Comput 2013;13(7):3324–34. [52] Dennis J, Schnabel R. Numerical methods for uncon-
[35] Hidayat MIP, Berata W. Neural networks with ra- strained optimization and nonlinear equations. Society
dial basis function and NARX structure for mate- for Industrial and Applied Mathematics; 1996.
rial lifetime assessment application. Adv Mater Res [53] Gendreau M, Potvin J. Handbook of metaheuristics.
2011;277:143–50. International series in operations research & manage-
[36] Wong CX, Worden K. Generalised NARX shunting ment science. US: Springer. ISBN 9781441916655, 2010.
neural network modelling of friction. Mech Syst Sig- [54] Du K, Swamy M. Search and optimization by
nal Process 2007;21:553–72. metaheuristics: Techniques and algorithms in-
[37] Potenza R, Dunne JF, Vulli S, Richardson D, King P. spired by nature. Springer International Publishing.
Multicylinder engine pressure reconstruction using ISBN 9783319411927, 2016.
NARX neural networks and crank kinematics. Int J [55] Glorot X, Bengio Y. Understanding the difficulty
Eng Res 2017;8:499–518. of training deep feedforward neural networks. In:
[38] Patel A, Dunne JF. NARX neural network modelling Teh YW, Titterington M, editors. Proceedings of the
of hydraulic suspension dampers for steady-state and Thirteenth International Conference on Artificial Intel-
variable temperature operation. Veh Syst Dyn: Int J ligence and Statistics. Proceedings of machine learning
Veh Mech Mobility 2003;40(5):285–328. research, vol. 9. Chia Laguna Resort, Sardinia, Italy:
[39] Gaya MS, Wahab NA, Sam YM, Samsudin SI, Ja- PMLR; 2010. p. 249–56. http://proceedings.mlr.press/
maludin IW. Comparison of NARX neural network v9/glorot10a.html.
and classical modelling approaches. Appl Mech Mater [56] Nocedal J. Updating quasi-Newton matrices with lim-
2014;554:360–5. ited storage. Math Comput 1980;35:773–82.
[40] Siegelmann HT, Horne BG, Giles CL. Computa- [57] Conn AR, Gould NIM, Toint PL. Trust-region methods.
tional capabilities of recurrent NARX neural net- Philadelphia, PA, USA: Society for Industrial and Ap-
works. IEEE Trans Syst Man Cybern, Part B, Cybern plied Mathematics. ISBN 0-89871-460-5, 2000.
1997;27(2):208–15. [58] Steihaug T. The conjugate gradient method and trust
[41] Kao CY, Loh CH. NARX neural networks for nonlinear regions in large scale optimization. SIAM J Numer
analysis of structures in frequency domain. J Chin Inst Anal 1983;20(3):626–37.
Eng 2008;31(5):791–804. [59] Martens J, Sutskever I. Learning recurrent neural net-
[42] Billings SA. Nonlinear system identification: NAR- works with Hessian-free optimization. In: Proceedings
MAX methods in the time, frequency and spatio- of the 28th International Conference on International
temporal domains. New York, NY: John Wiley & Sons; Conference on Machine Learning. USA: Omnipress.
2013. ISBN 978-1-4503-0619-5, 2011. p. 1033–40. http://dl.
[43] Pearson PK. Discrete-time dynamic models. New acm.org/citation.cfm?id=3104482.3104612.
York–Oxford: Oxford University Press; 1999. [60] Martens J, Sutskever I. Training deep and recurrent
[44] Nelles O. Nonlinear system identification: From classi- networks with Hessian-free optimization. In: Neu-
cal approaches to neural networks and fuzzy models. ral networks: Tricks of the trade. Springer; 2012.
Berlin: Springer; 2001. p. 479–535.
[45] Sutton RS, Barto AG. Reinforcement learning: An in- [61] Moré JJ. The Levenberg–Marquardt algorithm: Imple-
troduction. Cambridge, Massachusetts: The MIT Press; mentation and theory. In: Watson G, editor. Numer-
1998. ical analysis. Lecture notes in mathematics, vol. 630.
[46] Busoniu L, Babuška R, De Schutter B, Ernst D. Rein- Springer Berlin Heidelberg. ISBN 978-3-540-08538-6,
forcement learning and dynamic programming using 1978. p. 105–16.
function approximators. London: CRC Press; 2010. [62] Moré JJ, Sorensen DC. Computing a trust region step.
[47] Kamalapurkar R, Walters P, Rosenfeld J, Dixon W. Re- SIAM J Sci Stat Comput 1983;4(3):553–72. https://doi.
inforcement learning for optimal feedback control: A org/10.1137/0904038.
Lyapunov-based approach. Berlin: Springer; 2018. [63] Bottou L, Curtis F, Nocedal J. Optimiza-
[48] Lewis FL, Liu D. Reinforcement learning and approx- tion methods for large-scale machine learn-
imate dynamic programming for feedback control. ing. SIAM Rev 2018;60(2):223–311. https://
Hoboken, New Jersey: John Wiley & Sons; 2013. doi.org/10.1137/16M1080173.