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Performance Analyses of Recurrent Neural Network Models Exploited for Online Time-Varying Nonlinear Optimization

Mei Liu¹, Bolin Liao^2,3, Lei Ding^2,3 and Lin Xiao^2,3

1. College of Physics, Mechanical and Electrical Engineering, Jishou University
   Jishou, 416000, Hunan, China
   liumeijsu@163.com
2. College of Information Science and Engineering, Jishou University
   Jishou, 416000, Hunan, China
3. The Collaborative Innovation Center of Manganese-Zinc-Vanadium Industrial Technology (the 2011 Plan of Hunan Province)
   Jishou, 416000, Hunan, China
   mulinliao8184@163.com, 27279271@qq.com, xiaolin860728@163.com

Abstract

In this paper, a special recurrent neural network (RNN), i.e., the Zhang neural network (ZNN), is presented and investigated for online time-varying nonlinear optimization (OTVNO). Compared with the research work done previously by others, this paper analyzes continuous-time and discrete-time ZNN models theoretically via rigorous proof. Theoretical results show that the residual errors of the continuous-time ZNN model possesses a global exponential convergence property and that the maximal steady-state residual errors of any method designed intrinsically for solving the static optimization problem and employed for the online solution of OTVNO is O(τ ), where τ denotes the sampling gap. In the presence of noises, the residual errors of the continuous-time ZNN model can be arbitrarily small for constant noises and random noises. Moreover, an optimal sampling gap formula is proposed for discrete-time ZNN model in the noisy environments. Finally, computer-simulation results further substantiate the performance analyses of ZNN models exploited for online time-varying nonlinear optimization.

Key words

performance analysis, Zhang neural network (ZNN), online time-varying nonlinear optimization (OTVNO), Newton conjugate gradient model

Digital Object Identifier (DOI)

https://doi.org/10.2298/CSIS160215023L

Publication information

Volume 13, Issue 2 (June 2016)
Year of Publication: 2016
ISSN: 2406-1018 (Online)
Publisher: ComSIS Consortium

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How to cite

Liu, M., Liao, B., Ding, L., Xiao, L.: Performance Analyses of Recurrent Neural Network Models Exploited for Online Time-Varying Nonlinear Optimization. Computer Science and Information Systems, Vol. 13, No. 2, 691–705. (2016), https://doi.org/10.2298/CSIS160215023L