Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10138863 | Journal of Computational and Applied Mathematics | 2019 | 16 Pages |
Abstract
Time-varying nonlinear optimization (TVNO) problems are considered as important issues in various scientific disciplines and industrial applications. In this paper, the continuous-time derivative dynamics (CTDD) model is developed for obtaining the real-time solutions of TVNO problems. Furthermore, aiming to remedy the weaknesses of CTDD model, a continuous-time zeroing dynamics (CTZD) model is presented and investigated. For potential digital hardware realization, by using bilinear transform, a general four-step Zhang et al discretization (ZeaD) formula is proposed and applied to the discretization of both CTDD and CTZD models. A general four-step discrete-time derivative dynamics (general four-step DTDD) model and a general four-step discrete-time zeroing dynamics (general four-step DTZD) model are proposed on the basis of this general four-step ZeaD formula. Further theoretical analyses indicate that the general four-step DTZD model is zero-stable, consistent and convergent with the truncation error of O(g4), which denotes a vector with every entries being O(g4) with g denoting the sampling period. Theoretical analyses also indicate that the maximal steady-state residual error (MSSRE) has an O(g4) pattern confirmedly. The efficacy and accuracy of the general four-step DTDD and DTZD models are further illustrated by numerical examples.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Yunong Zhang, Liu He, Chaowei Hu, Jinjin Guo, Jian Li, Yang Shi,