Finite-Time Convergence and Robustness Analysis of Two Nonlinear Activated ZNN Models for Time-Varying Linear Matrix Equations

Xiao, Lin; Jia, Lei; Zhang, Yongsheng; Hu, Zeshan; Dai, Jianhua

doi:10.1109/access.2019.2941961

Cited by 20 publications

(7 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, the convergence and robustness of the CVRZNN model are theoretically analyzed in the presence of constant noise, linear noise, and random noise. In simulation examples, the GNN model [35], [36] and the ZNN model [37], [38] are applied to complex-valued matrix inversion for comparative purpose. The simulation results show that the state solution of the CVRZNN model can converge to the theoretical inversion of dynamic complex-valued matrix under external noises, while the ZNN model and the GNN model can hardly converge to theoretical inversion under the same conditions.…”

Section: Introductionmentioning

confidence: 99%

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

2020

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…(2011) and Xiao et al. (2019). Daily electricity generation data of the MSW incineration plant of Wuhan were used, from January 1, 2019, to April 20, 2020.…”

Section: Methodsmentioning

confidence: 96%

“…In order to determine the fraction for each component, we resolved a multivariate and nonhomogeneous linear equation, by using the caloric content as an independent variable and the eight components of MSW as dependent variables, including organic fraction, ash and stone, paper, plastics and rubber, textile, glass, metal, and wood. The least square method was used for finding the solutions of non-homogeneous linear equations, as suggested by Zhang et al (2011) and Xiao et al (2019). Daily electricity generation data of the MSW incineration plant of Wuhan were used, from January 1, 2019, to…”

Section: Inversion Algorithm Methodsmentioning

confidence: 99%

“…To find an optimal solution of PCMSW by the amount of harvested electricity, non‐homogeneous linear equations, which are widely used in chemistry research and aerial engineering (Xu, 2016), should be applied. The least square method has proven to be a feasible approach for finding the solutions of non‐homogeneous linear equations (Xiao et al., 2019; Zhang et al., 2011). According to our best knowledge, such algorithms for determining PCMSW by using the energy‐harvest data of incineration plants have rarely been discussed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A comparison study of bottom‐up and top‐down methods for analyzing the physical composition of municipal solid waste

Zhou

Xiao³

et al. 2021

J of Industrial Ecology

View full text Add to dashboard Cite

Municipal solid waste (MSW) management is a crucial issue in socioeconomic metabolism and requires multicategory and high‐resolution data, and data on the physical composition of municipal solid waste (PCMSW) are fundamental in MSW research. Extensive financial resources have been invested in the research on field investigations of PCMSW; however, it is time‐consuming and sometimes not truly representative of the studied case. In this work, two bottom‐up and two top‐down approaches were applied for analyzing the PCMSW, namely, field investigation (FI), BP neural network (BPNN), material flow analysis (MFA), and inversion algorithm based on electricity generation of waste incinerator (IAEI). Wuhan City, China, was chosen as the studied case for analyzing and comparing the PCMSW results. The PCMSW values obtained by applying those four methods showed acceptable differences, and the standard deviations of organic fraction, ash and stone, paper, plastic and rubber, textile, wood, metal, glass, and others were 3.94%, 2.77%, 6.57%, 2.22%, 2.49%, 1.36%, 0.53%, 1.19%, and 0.28%, respectively. Use of the MFA, BPNN, and IAEI methods could reduce time and labor spent on manual sampling, sorting, and weighing of MSW, compared to the FI method. BPNN algorithm advances in providing PCMSW data in history and by trajectory throughout the year, whereas IAEI contributes PCMSW data with much higher temporal resolution. Data quality and applicability of different methods were discussed, considering the availability of time, labor, and reference data.

show abstract

“…A global overview of Zeroing dynamical systems (ZND), involving ZND aimed to solving linear matrix equations, was presented in [12]. Nonlinear Zeroing neural dynamical systems with finitetime convergence and noise-tolerant for solving linear matrix equations in time-varying scenarios were proposed and investigated in [13,14]. A ZNN design whose dynamics are based on varying gain parameter and which are suitable for solving TV GLME was proposed in [15].…”

Section: Introductionmentioning

confidence: 99%

Recurrent Neural Network Models Based on Optimization Methods

et al. 2022

View full text Add to dashboard Cite

Many researchers have addressed problems involving time-varying (TV) general linear matrix equations (GLMEs) because of their importance in science and engineering. This research discusses and solves the topic of solving TV GLME using the zeroing neural network (ZNN) design. Five new ZNN models based on novel error functions arising from gradient-descent and Newton optimization methods are presented and compared to each other and to the standard ZNN design. Pseudoinversion is involved in four proposed ZNN models, while three of them are related to Newton’s optimization method. Heterogeneous numerical examples show that all models successfully solve TV GLMEs, although their effectiveness varies and depends on the input matrix.

show abstract

Finite-Time Convergence and Robustness Analysis of Two Nonlinear Activated ZNN Models for Time-Varying Linear Matrix Equations

Cited by 20 publications

References 37 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

A comparison study of bottom‐up and top‐down methods for analyzing the physical composition of municipal solid waste

Recurrent Neural Network Models Based on Optimization Methods

Contact Info

Product

Resources

About