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Performance analyses of recurrent neural network models exploited for online time-varying nonlinear optimization

Liu Mei (Jishou University, College of Physics, Mechanical and Electrical Engineering, Jishou, Hunan, China)
Liao Bolin (Jishou University, College of Information Science and Engineering, Jishou, Hunan, China + The Collaborative Innovation Center of Manganese-Zinc-Vanadium Industrial Technology (the Plan of Hunan Province), Jishou, Hunan, China)
Ding Lei (Jishou University, College of Information Science and Engineering, Jishou, Hunan, China + The Collaborative Innovation Center of Manganese-Zinc-Vanadium Industrial Technology (the Plan of Hunan Province), Jishou, Hunan, China)
Xiao Lin (Jishou University, College of Information Science and Engineering, Jishou, Hunan, China + The Collaborative Innovation Center of Manganese-Zinc-Vanadium Industrial Technology (the Plan of Hunan Province), Jishou, Hunan, China)

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.

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