Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations

Lin Xiao, Bolin Liao, Shuai Li, Ke Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

97 Citations (Scopus)

Abstract

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks.

Original languageEnglish
Pages (from-to)102-113
Number of pages12
JournalNeural Networks
Volume98
DOIs
Publication statusPublished - 1 Feb 2018

Keywords

  • Finite-time convergence
  • General time-varying linear matrix equations
  • Nonlinear activation functions
  • Nonlinear recurrent neural networks

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence

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