A recurrent neural network for solving Sylvester equation with time-varying coefficients

2002 ◽  
Vol 13 (5) ◽  
pp. 1053-1063 ◽  
Author(s):  
Yunong Zhang ◽  
Danchi Jiang ◽  
Jun Wang
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Sylvester Equation ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Varying Coefficients

A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation

2018 ◽  
Vol 48 (11) ◽  
pp. 3135-3148 ◽  
Author(s):  
Zhijun Zhang ◽  
Lunan Zheng ◽  
Jian Weng ◽  
Yijun Mao ◽  
Wei Lu ◽  
...  
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Sylvester Equation ◽  
Time Varying

scholarly journals An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 19291-19302 ◽  
Author(s):  
Lei Ding ◽  
Lin Xiao ◽  
Kaiqing Zhou ◽  
Yonghong Lan ◽  
Yongsheng Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Recurrent Neural Network ◽  
Neural Network Model ◽  
Sylvester Equation ◽  
Time Varying ◽  
Complex Valued

scholarly journals A new variant of the Zhang neural network for solving online time-varying linear inequalities

2012 ◽  
Vol 468 (2144) ◽  
pp. 2255-2271 ◽  
Author(s):  
Dongsheng Guo ◽  
Yunong Zhang
Keyword(s):  
Neural Network ◽  
Error Function ◽  
Time Derivative ◽  
Linear Inequalities ◽  
Time Varying ◽  
Design Formula ◽  
Varying Coefficients ◽  
New Variant ◽  
Zhang Neural Network ◽  
Time Varying Coefficients

Since March 2001, a special class of recurrent neural networks termed the Zhang neural network (ZNN) has been proposed by Zhang and co-workers for solving online a rich repertoire of time-varying problems. By extending Zhang et al. 's design formula (or say, the ZNN design formula), a (new) variant of the ZNN design formula is proposed and investigated in this paper, which is also based on a matrix/vector-valued indefinite error function. In addition, by employing such a novel design formula, a new variant of the ZNN (NVZNN) is proposed, developed and investigated for online solution of time-varying linear inequalities (LIs). The resultant NVZNN models are depicted in implicit dynamics and methodologically exploit the time-derivative information of time-varying coefficients. Computer simulation results further demonstrate the novelty, efficacy and superiority of the proposed NVZNN models for solving online time-varying LIs.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

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