Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 347, Issue -, Pages 314-329Publisher
ELSEVIER
DOI: 10.1016/j.cam.2018.08.017
Keywords
Time-varying nonlinear optimization; Derivative dynamics; Zeroing dynamics; Zhang et al. discretization; General ZeaD formula
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Funding
- National Natural Science Foundation of China [61473323]
- Foundation of Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, China [2013A07]
- Laboratory Open Fund of Sun Yat-sen University, China [20160209]
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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(g(4)), which denotes a vector with every entries being O(g(4)) with g denoting the sampling period. Theoretical analyses also indicate that the maximal steady-state residual error (MSSRE) has an O(g(4)) pattern confirmedly. The efficacy and accuracy of the general four-step DTDD and DTZD models are further illustrated by numerical examples. (C) 2018 Elsevier B.V. All rights reserved.
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