Improved neural solution for the Lyapunov matrix equation based on gradient search

Authors:
Yuhuan Chen;Chenfu Yi;Dengyu Qiao
Affiliations:
Center for Educational Technology, Gannan Normal University, Ganzhou 341000, China;Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China and School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, ...;Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
Venue:
Information Processing Letters
Year:
2013

Citing 9
Cited 0

A recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices

Computers & Mathematics with Applications
Letter: A functional neural network for computing the largest modulus eigenvalues and their corresponding eigenvectors of an anti-symmetric matrix

Neurocomputing
Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems

Computers & Mathematics with Applications
Gradient-based maximal convergence rate iterative method for solving linear matrix equations

International Journal of Computer Mathematics
Bi-criteria velocity minimization of robot manipulators using lvi-based primal-dual neural network and illustrated via puma560 robot arm

Robotica
An industrial study on the importance of software component documentation: A system integrator's perspective

Information Processing Letters
Improved gradient-based neural networks for online solution of Lyapunov matrix equation

Information Processing Letters
Design and analysis of a general recurrent neural network model for time-varying matrix inversion

IEEE Transactions on Neural Networks
Dynamics of a mean-shift-like algorithm and its applications on clustering

Information Processing Letters

Quantified Score

Hi-index	0.89

Visualization

Abstract

By using the hierarchical identification principle, based on the conventional gradient search, two neural subsystems are developed and investigated for the online solution of the well-known Lyapunov matrix equation. Theoretical analysis shows that, by using any monotonically-increasing odd activation function, the gradient-based neural networks (GNN) can solve the Lyapunov equation exactly and efficiently. Computer simulation results confirm that the solution of the presented GNN models could globally converge to the solution of the Lyapunov matrix equation. Moreover, when using the power-sigmoid activation functions, the GNN models have superior convergence when compared to linear models.