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

DOI10.1016/j.ipl.2011.05.010zbMath1260.68353OpenAlexW2013635942MaRDI QIDQ1944135

Yuhuan Chen, Zhongliang Lu, Chenfu Yi

Publication date: 4 April 2013

Published in: Information Processing Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ipl.2011.05.010

zbMATH Keywords

global convergenceLyapunov equationonline algorithmsanalysis of algorithmsreal-time systemsparallel processingactivation functiongradient-based neural networks

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Learning and adaptive systems in artificial intelligence (68T05) Online algorithms; streaming algorithms (68W27)

Related Items (16)

A novel robust fixed-time convergent zeroing neural network for solving time-varying noise-polluted nonlinear equations ⋮ Improved neural dynamics for online Sylvester equations solving ⋮ Signum-function array activated ZNN with easier circuit implementation and finite-time convergence for linear systems solving ⋮ Noise-tolerant continuous-time Zhang neural networks for time-varying Sylvester tensor equations ⋮ Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations ⋮ Design, verification and robotic application of a novel recurrent neural network for computing dynamic Sylvester equation ⋮ Control of pendulum tracking (including swinging up) of IPC system using zeroing-gradient method ⋮ Improved Zhang neural network with finite-time convergence for time-varying linear system of equations solving ⋮ Improved GNN method with finite-time convergence for time-varying Lyapunov equation ⋮ Convergence and robustness of bounded recurrent neural networks for solving dynamic Lyapunov equations ⋮ Improved neural solution for the Lyapunov matrix equation based on gradient search ⋮ A new type of recurrent neural networks for real-time solution of Lyapunov equation with time-varying coefficient matrices ⋮ Generalized reflexive and anti-reflexive solutions of the coupled Sylvester matrix equations via CD algorithm ⋮ Exact solutions and convergence of gradient based dynamical systems for computing outer inverses ⋮ An accelerated ZNN-based algorithm with piecewise time-varying parameters to solve time-variant linear equations ⋮ Infinitely many Zhang functions resulting in various ZNN models for time-varying matrix inversion with link to Drazin inverse

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finding iterative roots with a spiking neural network
• A gradient descent rule for spiking neurons emitting multiple spikes
• Time-varying square roots finding via Zhang dynamics versus gradient dynamics and the former's link and new explanation to Newton-Raphson iteration
• A recurrent neural network for real-time matrix inversion
• Analysis of noise-induced phase synchronization in nervous systems: from algorithmic perspective
• On the stability analysis of nonlinear systems using polynomial Lyapunov functions
• Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process
• Lyapunov matrix equations in system stability and control.
• Active boundary control of an Euler–Bernoulli beam for generating vibration-free state
• Gradient based iterative algorithms for solving a class of matrix equations

This page was built for publication: Improved gradient-based neural networks for online solution of Lyapunov matrix equation