Noise-Tolerant ZNN Models for Solving Time-Varying Zero-Finding Problems: A Control-Theoretic Approach

Jin, Long; Zhang, Yunong; Li, Shuai; Zhang, Yinyan

doi:10.1109/tac.2016.2566880

Cited by 193 publications

(43 citation statements)

References 22 publications

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“…It is worth pointing out that the above mentioned neural models do not consider noise interference in the process of solving matrix inversion, but in actual application scenarios, there are various uncertain noises. Hence, many researchers start to consider the design of noise-tolerant models in the study of neural networks [26]- [30]. For example, in [29], an integral-enhanced ZNN model is designed to solve the matrix inversion in the real domain under the interference of various external noises.…”

Section: Introductionmentioning

confidence: 99%

A Fully Complex-Valued and Robust ZNN Model for Dynamic Complex Matrix Inversion Under External Noises

2020

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Dynamic complex-valued matrix inversion is often used in the field of mathematics and engineering. Over the past years, many recurrent neural network models have been designed and researched to analyse the process of matrix inversion without noises interference. However, there are many types of uncertain noises in actual model design and analysis. In this article, a novel fully complex-valued and robust Zeroing neural network (CVRZNN) is firstly proposed for calculating the dynamic complex matrix inversion under the interference of external noise environment, and its robustness is analysed and demonstrated in the presence of various types of external noises. Compared with the previous zeroing neural network (ZNN) and the gradient neural network (GNN) for dynamic complex matrix inversion, this novel CVRZNN model has good robustness under three kinds of external noises. Besides, the theoretical analysis shows that the CVRZNN model can globally converge to zero under constant noise. Through comparative simulation results, the excellent performance of the proposed CVRZNN model is obviously demonstrated, which is much better than that of the previous GNN and ZNN models. INDEX TERMS Zeroing neural network (ZNN), gradient neural network, dynamic complex-valued matrix inversion, robustness, external noise.

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Section: Introductionmentioning

confidence: 99%

A Fully Complex-Valued and Robust ZNN Model for Dynamic Complex Matrix Inversion Under External Noises

2020

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“…where γ > 0, λ > 0. Due to the anti-noise property of (3), the application of ZNN models are extended in practical world [31], [32]. Two conclusions can be drawn from the aforementioned discussion.…”

Section: Introductionmentioning

confidence: 95%

Comprehensive Analysis of ZNN Models for Computing Complex-Valued Time-Dependent Matrix Inverse

2020

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Computing complex-valued time-dependent matrix inverse is an important procedure in statistics and control theory. Zeroing neural network (ZNN) becomes an effective method for solving timedependent issues. This paper proposes a complex-valued synthetical ZNN (CVSZNN) model for computing complex-valued time-dependent matrix inverse within different noise environments. Two important property is synthetically dissected in the construction process of CVSZNN model. First, the finite-time convergence, to ensure the efficiency of CVSZNN model for solving complex-valued time-dependent issue. Secondly, the anti-noise property, to guarantee the robustness of CVSZNN model in presence of noises. Two important aspects above have been validated by theoretical analysis and numerical experiments. Furthermore, the impact of parameters values is investigated based on the experimental results. As compared with the existing ZNN models for computing complex-valued time-dependent matrix inverse, the superiority of the proposed CVSZNN model is displayed fully. INDEX TERMS Zeroing neural network, time-dependent, finite-time convergence, complex-valued, antinoise, matrix inverse.

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“…Moreover, it is with convenience of hardware implementation [21]. Therefore, dynamic system approaches based on RNN have been regarded as an important and powerful tool for large-scale online applications [22]. Many neural-models have thus been put forward, investigated and exploited to solve online Moore-Penrose inverse [12][13][14]17].…”

Section: Introductionmentioning

confidence: 99%

Improved recurrent neural networks for online solution of Moore‐Penrose inverse applied to redundant manipulator kinematic control

Tan

Chen

et al. 2018

Asian Journal of Control

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In this paper, two novel neural networks (NNNs), namely NNN-L and NNN-R neural models, are proposed to online left and right Moore-Penrose inversion. As compared to GNN (gradient neural network) and the recently proposed ZNN (Zhang neural network) for the left or right Moore-Penrose inverse solving, our models are theoretically proven to possess superior global convergence performance. More importantly, the proposed NNN-R model is successfully applied to path-tracking control of a three-link planar robot manipulator. Illustrative examples well validate the theoretical analyses as well as demonstrate the feasibility of the proposed models, which are adopted and verified their effectiveness in kinematic control of a redundant manipulator, for real-time Moore-Penrose inverse solving.

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Noise-Tolerant ZNN Models for Solving Time-Varying Zero-Finding Problems: A Control-Theoretic Approach

Cited by 193 publications

References 22 publications

A Fully Complex-Valued and Robust ZNN Model for Dynamic Complex Matrix Inversion Under External Noises

A Fully Complex-Valued and Robust ZNN Model for Dynamic Complex Matrix Inversion Under External Noises

Comprehensive Analysis of ZNN Models for Computing Complex-Valued Time-Dependent Matrix Inverse

Improved recurrent neural networks for online solution of Moore‐Penrose inverse applied to redundant manipulator kinematic control

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