Constrained Quaternion-Variable Convex Optimization: A Quaternion-Valued Recurrent Neural Network Approach

Liu, Yang; Zheng, Yingqin; Lu, Jianquan; Cao, Jinde; Rutkowski, Leszek

doi:10.1109/tnnls.2019.2916597

Cited by 103 publications

(50 citation statements)

References 43 publications

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“…On the other hand, complex signals exist in most NN applications in the real world. As such, multidimensional problems such as color night vision, radar imaging, polarized signal classification, 3D wind forecasting can be solved more favorably by implementing complex-valued and quaternion-valued NN models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. To date, several important results regarding various dynamics of complex-valued and quaternion-valued NN models have been published, some of them stability analysis [13,14,[20][21][22]26], synchronization analysis [11], stabilizability and instabilizability [12], controllability and observability [23], optimization [24,25] and so on.…”

Section: Introductionmentioning

confidence: 99%

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

et al. 2021

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In this study, we investigate the global exponential stability of Clifford-valued neural network (NN) models with impulsive effects and time-varying delays. By taking impulsive effects into consideration, we firstly establish a Clifford-valued NN model with time-varying delays. The considered model encompasses real-valued, complex-valued, and quaternion-valued NNs as special cases. In order to avoid the issue of non-commutativity of the multiplication of Clifford numbers, we divide the original n-dimensional Clifford-valued model into $2^{m}n$ 2 m n -dimensional real-valued models. Then we adopt the Lyapunov–Krasovskii functional and linear matrix inequality techniques to formulate new sufficient conditions pertaining to the global exponential stability of the considered NN model. Through numerical simulation, we show the applicability of the results, along with the associated analysis and discussion.

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Section: Introductionmentioning

confidence: 99%

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

et al. 2021

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“…3 At present, QVNNs have been studied in many fields, such as image processing, 4 optimization control. 5 Quaternions, discovered by a British mathematician William Rowan Hamilton in 1843, were the first discovered noncommutative division algebra. They are much more difficult to research than the complex ones, so the development of quaternions is particularly slow before.…”

Section: Introductionmentioning

confidence: 99%

“…Up to now, some people are studying the optimization of constrained convex functions with quaternion variables. 20 But most scholars focus on the global behaviors of QVNNs. When dealing with quaternions, the complex decomposition method and Lyapunov stability theory are basically used to obtain the unified criterion for the stability in continuous and discrete time.…”

Section: Introductionmentioning

confidence: 99%

“…In order to directly process the three‐dimensional data, quaternion‐valued neural networks (QVNNs) are proposed as a result 3 . At present, QVNNs have been studied in many fields, such as image processing, 4 optimization control 5 …”

Section: Introductionmentioning

confidence: 99%

“…Up to now, some people are studying the optimization of constrained convex functions with quaternion variables 20 . But most scholars focus on the global behaviors of QVNNs.…”

Section: Introductionmentioning

confidence: 99%

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A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

Lou

et al. 2020

Intl J Robust & Nonlinear

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In this article, the stability of quaternion-valued neural networks (QVNNs) with hybrid impulses is investigated, which contain stabilizing impulses and destabilizing impulses simultaneously. Through constructing the relationship between impulses and quaternions, this article has obtained a unified criterion for the global exponential stability of the system. First, a new form of impulsive representation is constructed, and the established systems can be decomposed into four different real parts. According to the characteristics of the impulses, the system divides the average interval of impulses (AII) into two cases, that is, T < ∞ and T = ∞, which can process hybrid impulses simultaneously. Second, for QVNNs, by using the method of matrix p-norm and the inequality technology, the criterion of each interval is derived. Considering the impulsive effects on the overall stability of QVNNs, the uniform criterion for the global exponential stability can be obtained. In addition, the convergence rate of QVNNs with hybrid impulses is also discussed. Finally, in order to verify the theoretical conclusions, some numerical simulations are given.

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Lagrange exponential stability of quaternion‐valued memristive neural networks with time delays

Wei

Cao

Huang

2020

Math Methods in App Sciences

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This paper investigates the Lagrange global exponential stability of the quaternion‐valued memristive neural networks (QVMNNs). Two kinds of activation functions based on different assumptions are considered. Then, based on the Lyapunov function approach, decomposition method, and some inequality skills, two novel sufficient conditions for lagrange stability of QVMNNs are provided corresponding to different types of activation functions. Lastly, simulation examples are provided to demonstrate the correctness of our theoretical results.

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Constrained Quaternion-Variable Convex Optimization: A Quaternion-Valued Recurrent Neural Network Approach

Cited by 103 publications

References 43 publications

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

Lagrange exponential stability of quaternion‐valued memristive neural networks with time delays

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