An exponential evaluation for recurrent neural network with discrete delays
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2019.2.07Keywords:
recurrent neural network, delay differential equations, exponential stability, Lyapunov functionalAbstract
The purpose of this study is to develop and apply a method for calculating the exponential fade rate for a model of a recurrent neural network based on discrete latency differential equations. An exponential estimate is obtained on the basis of the difference inequality for the Lyapunov function. An example of the exponential estimation for a model of a recurrent neural network with three neurons is presented.References
Amato Filippo. Artificial neural networks in medical diagnosis / Filippo Amato, Alberto López, Eladia María Peña-Méndez et al. // Journal of Applied Biomedicine. — 2013. — Vol. 11, Issue 2. — P. 47–58. — https://doi.org/10.2478/v10136-012-0031-x.
Jančíková Z.K. Review on Artificial Intelligence Applications in Material Diagnostics and Technology / Z.K. Jančíková, P. Koštial, M. Heger et al. — (2018) MATEC Web of Conferences, 210, art. no. 04030. DOI: 10.1051/matecconf/ 201821004030.
Pliego Marugán Alberto. A survey of artificial neural network in wind energy systems / Alberto Pliego Marugán, Fausto Pedro GarcĂa Márquez, Jesus MarĂa Pinar Perez, Diego Ruiz-Hernández // Applied Energy. — 2018. — Vol. 228. — P. 1822–1836. — https://doi.org/10.1016/j.apenergy.2018.07.084.
Sieniutycz Stanislaw. A Review of Applications Optimizing Thermal, Chemical, and Environmental Systems / Stanislaw Sieniutycz, Zbigniew Szwast // Elsevier. — 2018. — P. 109–120. — https://doi.org/10.1016/B978-0-12-813582-2.00004-5.
Qin C. Computer-aided detection in chest radiography based on artificial intelligence: A survey / C. Qin, D. Yao, Y. Shi, Z. Song // BioMedical Engineering Online. — 2018. — 17 (1), art. no. 113. — DOI: 10.1186/s12938-018-0544-y
Rajendra Acharya U. Deep convolutional neural network for the automated detection and diagnosis of seizure using EEG signals / U. Rajendra Acharya, Shu Lih Oh, Yuki Hagiwara et al. // Computers in Biology and Medicine. — 2018. — Vol. 100. — P. 270–278. — https://doi.org/10.1016/j.compbiomed.2017.09.017.
Deng Hongli. Feature memory-based deep recurrent neural network for language modeling / Hongli Deng, Lei Zhang, Xin Shu // Applied Soft Computing. — 2018. — Vol. 68. — P. 432–446. — https://doi.org/10.1016/j.asoc.2018.03.040.
Plappert Matthias. Learning a bidirectional mapping between human whole-body motion and natural language using deep recurrent neural networks / Matthias Plappert, Christian Mandery, Tamim Asfour // Robotics and Autonomous Systems. — 2018. — Vol. 109. — P. 13–26. — https://doi.org/10.1016/j. robot.2018.07.006.
Park J.H. On global stability criterion for neural networks with discrete and distributed delays / J.H. Park // Chaos, Solitons & Fractals. — 2006. — Vol. 30, N 4. — P. 897–902. — Available at: http://dx.doi.org/10.1016/j.chaos.2005.08.147.
Park J.H. A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays / J.H. Park, H.J. Cho // Chaos, Solitons & Fractals. — 2007. — Vol. 33, N 2. — P. 436–442. — Available at: http://dx. doi.org/10.1016/j.chaos.2006.01.015.
Liao X. Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach / X. Liao, G. Chen, E.N. Sanchez // Neural Networks. — 2002. — Vol. 15, N 7. — P. 855–866. — Available at: http://dx.doi.org/10.1016/ S0893-6080(02)00041-2.
Haykin Simon. Neural Networks and Learning Machines: A Comprehensive Foundation (3rd Edition) / Simon Haykin. — 2011. — 936 p.
Marcus C.M. Stability of analog neural networks with delay / C.M. Marcus, R.M. Westervelt // Physical Review A. — 1989, 39.1: 347.
He Y. Delay-range-dependent stability for systems with time-varying delay / Y. He, Q.G. Wang, C. Lin, M. Wu // Automatica. — 2007. — Vol. 43, N 2. — P. 371–376. — Available at: http://dx.doi.org/10.1016/j.automatica.2006.08.015.
Lien C.-H. Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays / C.-H. Lien, L.-Y. Chung // Chaos, Solitons & Fractals. — 2007. — Vol. 34, N 4. — P. 1213–1219. — Available at: http://dx.doi.org/ 10.1016/j.chaos.2006.03.121.
Zhang Q. Stability of delayed cellular neural networks / Q. Zhang, X. Wei, J. Xu // Chaos, Solitons & Fractals. — 2007. — Vol. 31, N 2. — P. 514–520. — Available at: http://dx. doi.org/10.1016/j.chaos.2005.10.003.
Singh V. New global robust stability results for delayed cellular neural networks based on norm-bounded uncertainties / V. Singh // Chaos, Solitons & Fractals. — 2006. — Vol. 30, N 5. — P. 1165–1171. — Available at: http://dx.doi.org/ 10.1016/j.chaos.2005.08.183.
Martsenyuk V. On an indirect method of exponential estimation for a neural network model with discretely distributed delays / V. Martsenyuk // Electronic Journal of Qualitative Theory of Differential Equations. — 2017. — N 23. — P. 1–16.
Indirect method of exponential convergence estimation for neural network with discrete and distributed delays // Electronic Journal of Differential Equations. — 2017.
Khusainov D. Two-side estimates of solutions of linear systems with delay / D. Khusainov, V. Marzeniuk // Reports of Ukr. Nat. Acad. Sciences. — 1996. — P. 8–13.
Kertesz V. Stability investigations and exponential estimations for functional differential equations of retarded type / V. Kertesz // Acta Mathematica Hungarica. — 1990. — Vol. 55, N 3–4. — P. 365–378.
Hale J.K. Introduction to functional differential equations / J.K. Hale, S.M.V. Lunel // Springer Science & Business Media. — 2013. — Vol. 99.
Cao J. Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays / J. Cao, J. Wang // Neural Netw. — 2004. — 17, N 3. — P. 379–390.
