Discrete-Time ZND Models Solving ALRMPC via Eight-Instant General and Other Formulas of ZeaD

Chen, Jianrong; Zhang, Yunong

doi:10.1109/access.2019.2938840

Cited by 13 publications

(5 citation statements)

References 31 publications

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“…By setting the values of the three parameters in [24] as η 1 = η 3 = 0 and η 2 = −9/10, respectively, the following eight-instant ZeaD formula can be obtained:…”

Section: Eleven-instant and Other Zead Formulasmentioning

confidence: 99%

“…In order to facilitate the implementation of modern electronic hardware, the continuous model needs to be discretized. Therefore, in recent years, a new class of finite difference formula, termed Zhang et al discretization (ZeaD) formula [17][18][19][20][21][22][23][24], has been proposed and used to discretize a continuous model into a discrete one.…”

Section: Introductionmentioning

confidence: 99%

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Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

Chen,

Kang,

Zhang

2023

Mathematics

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The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models.

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“…By setting the values of the three parameters in [24] as η 1 = η 3 = 0 and η 2 = −9/10, respectively, the following eight-instant ZeaD formula can be obtained:…”

Section: Eleven-instant and Other Zead Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

Chen,

Kang,

Zhang

2023

Mathematics

Self Cite

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show abstract

“…where O(η 2 ) denotes the second-order truncation error. e last discretization formula employed in this paper is an 8-instant ZeaD formula [44]…”

Section: Discretization Formulasmentioning

confidence: 99%

New Models for Solving Time-Varying LU Decomposition by Using ZNN Method and ZeaD Formulas

Ming

Zhang

Liu

et al. 2021

Journal of Mathematics

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In this paper, by employing the Zhang neural network (ZNN) method, an effective continuous-time LU decomposition (CTLUD) model is firstly proposed, analyzed, and investigated for solving the time-varying LU decomposition problem. Then, for the convenience of digital hardware realization, this paper proposes three discrete-time models by using Euler, 4-instant Zhang et al. discretization (ZeaD), and 8-instant ZeaD formulas to discretize the proposed CTLUD model, respectively. Furthermore, the proposed models are used to perform the LU decomposition of three time-varying matrices with different dimensions. Results indicate that the proposed models are effective for solving the time-varying LU decomposition problem, and the 8-instant ZeaD LU decomposition model has the highest precision among the three discrete-time models.

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“…delays [25]- [29]. Specifically, when these methods are utilized to solve TVLES, they must be viewed as static at different time instants.…”

Section: Introductionmentioning

confidence: 99%

Stability-Constraint-Free Solutions to Solve Time-Varying Linear Equation System

Fan

Zhu

et al. 2022

IEEE Access

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Time-varying linear equation systems have been solved by the traditional zeroing neural dynamics approach in recent years. However, this method has to satisfy the stability constraint, which is a very rigorous condition. For this reason, traditional Lagrange-type finite difference formulas fail to lead to effective solutions, and we have to utilize more instants and reduce accuracy so that this condition is satisfied. In this work, we develop a new method of solving a time-varying linear equation system, which is based on theoretical solution decomposition. As a result, the proposed solutions are stability-constraint-free. We do not have to meticulously search effective time-discretization formulas because traditional Lagrange-type formulas are sufficient and especially effective. In addition, the proposed solutions have other advantages. For example, they do not need convergence procedures; they do not have storage requirements for past calculative results; and they are still effective when the sampling gap value is relatively large. Detailed comparisons are presented in this paper. Comparative numerical experiments are also shown to substantiate the effectiveness and advantages of the proposed solutions.

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Discrete-Time ZND Models Solving ALRMPC via Eight-Instant General and Other Formulas of ZeaD

Cited by 13 publications

References 31 publications

Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

New Models for Solving Time-Varying LU Decomposition by Using ZNN Method and ZeaD Formulas

Stability-Constraint-Free Solutions to Solve Time-Varying Linear Equation System

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