New Models for Future Problems Solving by Using ZND Method, Correction Strategy and Extrapolation Formulas

Zhiyuan Qi

doi:10.1109/ACCESS.2019.2924469

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New Models for Future Problems Solving by Using ZND Method, Correction Strategy and Extrapolation Formulas

2019-01-01

Zhiyuan Qi

Yunong Zhang *

DOI：10.1109/ACCESS.2019.2924469

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Abstract

En 中文

Time-variant problems, which can be classified into future and non-future problems, are often encountered in academia and industry. In a future problem, we only know the information on the current and past time instants, and we have to acquire the next-time-instant solution before the next time instant arrives. Zeroing neural dynamics (ZND) and Zhang et al. discretization (ZeaD) formula group are two essential tools to build discrete-time ZND (DT-ZND) models for future problems solving. The former uses a systematical design formula to build a continuous-time ZND (CT-ZND) model, and the latter is used to transform the CT-ZND model into the discrete-time forms. Many DT-ZND models have been developed to solve various time-variant problems. In light of DT-ZND models and correction strategy, in this paper, we mainly focus on designing and building improved models for future problems solving. Based on the ZND method, extrapolation formulas, and correction steps, new models and corresponding computational algorithms are proposed to solve future optimization and future matrix inversion problems. The numerical experiments are also carried out to demonstrate the superiority of the proposed algorithms.

Keywords:

Future problem

zeroing neural dynamics (ZND)

correction strategy

extrapolation formula

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