A parallel computing method based on zeroing neural networks for time-varying complex-valued matrix Moore-Penrose inversion

Xiao, Xiuchun; Jiang, Chengze; Lu, Huosheng; Jin, Long; Liu, Dazhao; Huang, Haoen; Pan, Yi

doi:10.1016/j.ins.2020.03.043

Cited by 44 publications

(37 citation statements)

References 36 publications

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“…In reference [42], a TVDZNN is designed to realize matrix inversion. In reference [43], a CVZNN is used for dynamic Moore-Penrose inverse solving, and it relaxes convex constraint of the AF. However, all the above mentioned works only consider the ideal no noise condition, and their robustness is unpredictable in noisy environment.…”

Section: Introductionmentioning

confidence: 99%

Design and Analysis of Anti-Noise Parameter-Variable Zeroing Neural Network for Dynamic Complex Matrix Inversion and Manipulator Trajectory Tracking

Zhou

Tan

2022

Electronics

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Dynamic complex matrix inversion (DCMI) problems frequently arise in the territories of mathematics and engineering, and various recurrent neural network (RNN) models have been reported to effectively find the solutions of the DCMI problems. However, most of the reported works concentrated on solving DCMI problems in ideal no noise environment, and the inevitable noises in reality are not considered. To enhance the robustness of the existing models, an anti-noise parameter-variable zeroing neural network (ANPVZNN) is proposed by introducing a novel activation function (NAF). Both of mathematical analysis and numerical simulation results demonstrate that the proposed ANPVZNN model possesses fixed-time convergence and robustness for solving DCMI problems. Besides, a successful ANPVZNN-based manipulator trajectory tracking example further verifies its robustness and effectiveness in practical applications.

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Section: Introductionmentioning

confidence: 99%

Design and Analysis of Anti-Noise Parameter-Variable Zeroing Neural Network for Dynamic Complex Matrix Inversion and Manipulator Trajectory Tracking

Zhou

Tan

2022

Electronics

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“…By making full use of the time derivative information of time-varying parameters, the theoretical solution to the timevarying problems is tracked by the evolution formula. Taking advantage of the method of ZNN [20]- [22], the objective of effectively solving time-varying problems is achieved. Specifically, Xu et al [23] furnish a ZNN model for ensuring the solution of the TVLEI problem, which takes full advantage of the ZNN model as well as the time-derivative information about the time-varying coefficients involved in the time-varying problems.…”

Section: Introductionmentioning

confidence: 99%

Solving Perturbed Time-Varying Linear Equation and Inequality Problem With Adaptive Enhanced and Noise Suppressing Zeroing Neural Network

Huang

et al. 2022

IEEE Access

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Solving time-varying linear equation and inequality (TVLEI) problem has attracted extensive attention in numerous scientific and engineered fields. In this article, it is basically considered that the commonly used dynamics neural network in the virtual environment is inevitably interfered with by the variable measurement noises while dealing with the TVLEI problem. An adaptive enhanced and noisesuppressing zeroing neural network (AENSZNN) model is proposed as an improved algorithm for solving the TVLEI problem. An adaptive scale factor based on the residual error norm is designed to make the proposed AENSZNN model converge to the theoretical solution faster. Furthermore, the momentum enhancement terms added to the model enables the AENSZNN model to effectively solve the TVLEI problem in real-time under the obstruction of different measurement noises. Besides, theoretical results and numerical experiments indicate that the AENSZNN model has advantages in convergence accuracy and robustness to noises compared with the existing algorithms. Note that, the proposed AENSZNN model is successfully exploited for the estimation of mobile object localization.

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“…Therefore, this paper proposes adaptive coefficients [33] to construct a adaptive coefficient and non-convex projection zeroing neural network (ACN-PZNN) model, which not only can overcome the excessively long convergence time and convergence accuracy of the ZNN model, but also achieve the effect of adaptive system changes. Then, this paper applies the saturation function as the activation activation of the ACNPZNN model, and further shortens the convergence time on the basis of the ACNPZNN model by reading the literature [34]- [36]. Furthermore, considering the convex constraint problem, this paper uses a non-convex bound activation function to activate the ACNPZNN model and to relax the convex constraint.…”

Section: Introductionmentioning

confidence: 99%

Solving Time-Varying Complex-Valued Sylvester Equation via Adaptive Coefficient and Non-Convex Projection Zeroing Neural Network

Jiang

Chen

et al. 2021

IEEE Access

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The time-varying complex-valued Sylvester equation (TVCVSE) often appears in many fields such as control and communication engineering. Classical recurrent neural network (RNN) models (e.g., gradient neural network (GNN) and zeroing neural network (ZNN)) are often used to solve such problems. This paper proposes an adaptive coefficient and non-convex projection zeroing neural network (ACNPZNN) model for solving TVCVSE. To enhance its adaptability as residual error decreasing as time, an adaptive coefficient is designed based on residual error. Meanwhile, this paper breaks the convex constraint by constructing two complex-valued non-convex projection activation functions from two different aspects. Moreover, the global convergence of the proposed model is proved, the anti-noise performance of the ACNPZNN model under different noises is theoretically analyzed. Finally, simulation experiments are provided to compare the convergence performance of different models, which simultaneously verifies the effectiveness and superiority of the proposed model. INDEX TERMS Time-varying complex-valued Sylvester equation (TVCVSE), Zeroing neural network (ZNN), Adaptive coefficient, Non-convex projection.

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A parallel computing method based on zeroing neural networks for time-varying complex-valued matrix Moore-Penrose inversion

Cited by 44 publications

References 36 publications

Design and Analysis of Anti-Noise Parameter-Variable Zeroing Neural Network for Dynamic Complex Matrix Inversion and Manipulator Trajectory Tracking

Design and Analysis of Anti-Noise Parameter-Variable Zeroing Neural Network for Dynamic Complex Matrix Inversion and Manipulator Trajectory Tracking

Solving Perturbed Time-Varying Linear Equation and Inequality Problem With Adaptive Enhanced and Noise Suppressing Zeroing Neural Network

Solving Time-Varying Complex-Valued Sylvester Equation via Adaptive Coefficient and Non-Convex Projection Zeroing Neural Network

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