MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Time-Varying Lyapunov Equation Solving

Zhang, Yunong; Yue, Shuai; Chen, Ke; Chen, Yi

doi:10.1007/978-3-540-87732-5_14

Cited by 9 publications

(11 citation statements)

References 16 publications

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“…In addition to Proposition 1, if a linear activation-function array F (·) is used, then neuralstate matrix P (t) of ZNN (4) starting from any initial state P 0 ∈ R n×n could exponentially converge to the theoretical time-varying solution P * (t) of (1) with rate γ. If the array F (·) made up of n 2 power-sigmoid activation functions (4) is used, then superior global exponential convergence can be achieved for ZNN (4), as compared to the situation of using linear activation functions.…”

Section: Neural-network Solversmentioning

confidence: 99%

“…That is, in this time-varying context, gradient-based neural networks only approximately converge to the theoretical solution P * (t) with appreciable residual errors [3]. To remedy, a special kind of recurrent neural network could be generalized from [3][4][5] for solution of this time-varying matrix problem in real-time.…”

Section: Introductionmentioning

confidence: 99%

“…However, many time-varying problems intrinsically exist in scientific, engineering, business and even social computational areas [2][3][4][5], such as, the time-varying Lyapunov equation solving depicted as below:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulink Modeling and Comparison of Zhang Neural Networks and Gradient Neural Networks for Time-Varying Lyapunov Equation Solving

Zhang

Chen

et al. 2008

2008 Fourth International Conference on Natural Computation

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In view of the great potential in parallel processing and ready implementation via hardware, neural networks are now often employed to solve online matrix algebraic problems. Recently, a special kind of recurrent neural network has been proposed by Zhang et al, which could be generalized to solving online Lyapunov equation with time-varying coefficient matrices. In comparison with gradient-based neural networks (GNN), the resultant Zhang neural networks (ZNN) perform much better on solving these timevarying problems. This paper investigates the MATLAB Simulink modeling, simulative verification and comparison of ZNN and GNN models for time-varying Lyapunov equation solving. Computer-simulation results verify that superior convergence and efficacy could be achieved by such ZNN models when solving the time-varying Lyapunov matrix equation, as compared to the GNN models.

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Section: Neural-network Solversmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simulink Modeling and Comparison of Zhang Neural Networks and Gradient Neural Networks for Time-Varying Lyapunov Equation Solving

Zhang

Chen

et al. 2008

2008 Fourth International Conference on Natural Computation

Self Cite

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“…One conventional neural network, termed as gradient-based neural network (GNN) (Zhang, 2005;Zhang, Chen, Ma, & Li, 2007;Zhang & Wang, 2002), based on gradient-descend method to minimize normbased bounded energy function, has already been employed comprehensively to solve such static problems. However, when such a GNN method is applied to solve a time-varying (coefficients) case, a faster convergence rate is often required when compared to the variational rate of time-varying coefficients in real time (Zhang & Ge, 2005;Zhang, Yue, Chen, & Yi, 2008). This may thus impose stringent restrictions on physical realization and/or sacrifice the solution precision.…”

Section: Introductionmentioning

confidence: 94%

Improved Zhang neural network model and its solution of time-varying generalized linear matrix equations

Zhang

2010

Expert Systems with Applications

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“…In this method, by using an optimization algorithm, the samples which form the class borders will be achieved, which call backup vectors. Teaching points that are closest to the point of decision-making can be considered as a subset to define boundaries for decision-making and to be a support vector [39].…”

Section: Support Vector Machinementioning

confidence: 99%

Analysis of Heart Rate Dynamics Before and During Meditation

2021

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Heart rate is one of the most important vital signs. People usually face high tension in routine life, and if we found an effective method to control the heart rate, it would be very desirable. One of the goals of this paper is to examine changes in heart rate before and during meditation. Another goal is that what impact could have meditation on the human heartbeat.To heart rate analysis before and during meditation, available heart rate signals have been used for the Physionet database that contains 10 normal subjects and 8 subjects that meditation practice has been done on them. In this paper, first is paid to extract linear and nonlinear characteristics of heart rate and then is paid to the best combination of features to identify two intervals before and during meditation using MLP and SVM classifiers with the help of sensitivity, specificity and accuracy measurements.The achieved results in this paper showed that choosing the best combination of a feature to make a meaningful difference between two intervals before and during meditation includes two-time features (Mean HR, SDNN), a frequency feature ( ), and three nonlinear characteristics ( ). Also, using the support vector machine had better results than the MLP neural network. The sensitivity, specificity, and accuracy of the mean and standard deviation obtained respectively like 92.73 0.23, 89.05 0.67, 89.97 0.23 by using MLP and respectively like 95.96 0.09, 93.80 0.16, and 94.90 0.14 by using SVM.As a result, using meditation can reduce the stress and anxiety of patients by effects on heart rate, and the treatment process speeds up and have an important role in improving the performance of the system.

show abstract

MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Time-Varying Lyapunov Equation Solving

Cited by 9 publications

References 16 publications

Simulink Modeling and Comparison of Zhang Neural Networks and Gradient Neural Networks for Time-Varying Lyapunov Equation Solving

Simulink Modeling and Comparison of Zhang Neural Networks and Gradient Neural Networks for Time-Varying Lyapunov Equation Solving

Improved Zhang neural network model and its solution of time-varying generalized linear matrix equations

Analysis of Heart Rate Dynamics Before and During Meditation

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