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

DOI10.1016/j.ipl.2013.09.002zbMath1284.68492OpenAlexW2011703186MaRDI QIDQ2445328

Dengyu Qiao, Yuhuan Chen, Chenfu Yi

Publication date: 14 April 2014

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

Full work available at URL: https://doi.org/10.1016/j.ipl.2013.09.002

zbMATH Keywords

analysis of algorithmsenergy functionrecurrent neural networkshierarchical identification principleactivation functiongradient search

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Learning and adaptive systems in artificial intelligence (68T05) Iterative numerical methods for linear systems (65F10)

Related Items (13)

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 ⋮ Zhang neural networks for a set of linear matrix inequalities with time-varying coefficient matrix ⋮ Improved SOR iterative method for coupled Lyapunov matrix equations ⋮ General recurrent neural network for solving generalized linear matrix equation ⋮ Design, verification and robotic application of a novel recurrent neural network for computing dynamic Sylvester equation ⋮ Improved Zhang neural network with finite-time convergence for time-varying linear system of equations solving ⋮ Lower Eigenvalue Bounds on Summation for the Solution of the Lyapunov Matrix Differential Equation ⋮ On the convergence of conjugate direction algorithm for solving coupled Sylvester matrix equations ⋮ Convergence of HS version of BCR algorithm to solve the generalized Sylvester matrix equation over generalized reflexive matrices ⋮ The eigenvalue product bounds of the Lyapunov matrix differential equation and the stability of a class of time-varying nonlinear system ⋮ Infinitely many Zhang functions resulting in various ZNN models for time-varying matrix inversion with link to Drazin inverse ⋮ Gradient-based neural networks for solving periodic Sylvester matrix equations

Cites Work

• Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling
• Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems
• Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model
• Dynamics of a mean-shift-like algorithm and its applications on clustering
• Improved gradient-based neural networks for online solution of Lyapunov matrix equation
• A recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices
• Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process
• Active boundary control of an Euler–Bernoulli beam for generating vibration-free state
• Kalman filter-based identification for systems with randomly missing measurements in a network environment
• Gradient based iterative algorithms for solving a class of matrix equations
• The ensemble Kalman filter for combined state and parameter estimation
• Gradient-based maximal convergence rate iterative method for solving linear matrix equations

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