Title :
A recurrent neural network for solving Sylvester equation with time-varying coefficients
Author :
Zhang, Yunong ; Jiang, Danchi ; Wang, Jun
Author_Institution :
Dept. of Autom. & Comput.-Aided Eng., Chinese Univ. of Hong Kong, Shatin, China
fDate :
9/1/2002 12:00:00 AM
Abstract :
Presents a recurrent neural network for solving the Sylvester equation with time-varying coefficient matrices. The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation. Theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network. Simulation results of time-varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network.
Keywords :
convergence; matrix inversion; nonlinear control systems; pendulums; pole assignment; recurrent neural nets; Sylvester equation; ball and beam system; cart system; global exponential convergence; implicit dynamics; inverted pendulum; linear matrix equation; online nonlinear output regulation; pole assignment; recurrent neural network; sensitivity analysis; time-varying coefficient matrices; time-varying matrix inversion; Control system synthesis; Control systems; Cost function; Helium; Network synthesis; Neural networks; Nonlinear equations; Recurrent neural networks; Sensitivity analysis; Time varying systems;
Journal_Title :
Neural Networks, IEEE Transactions on
DOI :
10.1109/TNN.2002.1031938
