A recurrent neural network for solving Sylvester equation with time-varying coefficients |
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Authors: | Yunong Zhang Danchi Jiang Jun Wang |
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Affiliation: | Dept. of Autom. & Comput.-Aided Eng., Chinese Univ. of Hong Kong, Shatin; |
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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. |
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