Gene

Quantum mechanics

Robot

Chaotic

Applied mathematics

Robustness (evolution)

Eigenvalues and eigenvectors

Biochemistry

Computer science

Sylvester equation

Physics

Lyapunov equation

Mathematics

Lyapunov exponent

Artificial intelligence

Chemistry

Artificial neural network

Recurrent neural network

Speech recognition

IEEE Transactions on Industrial Informatics

A generalized Sylvester equation is a special formulation containing the Sylvester equation, the Lyapunov equation and the Stein equation, which is often encountered in various fields. However, the time-variant generalized Sylvester equation (TVGSE) is rarely investigated in the existing literature. In this article, we propose a noise-suppressing recurrent neural network (NSRNN) model activated by saturation-allowed functions to solve the TVGSE. For comparison, the existing zeroing neural network (ZNN) models and some improved ZNN models are introduced. Additionally, theoretical analysis on the convergence and robustness of the NSRNN model is given. Furthermore, computer simulations on illustrative examples and applications to robots and acoustic source localization are carried out. Validation results synthesized by the NSRNN model and other ZNN models are provided to illustrate the ability in solving the TVGSE and dealing with noises of the NSRNN model, and the inaction of other ZNN models to noises.

RNN for Solving Time-Variant Generalized Sylvester Equation With Applications to Robots and Acoustic Source Localization