Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations. (February 2018)

• Record Type: Journal Article
• Authors: Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke
• Is Part Of: Neural networks. Volume 98(2018)
• Page Start: 102
• Page End: 113
• Publication Date: 2018-02
• Subjects: Nonlinear recurrent neural networks -- General time-varying linear matrix equations -- Finite-time convergence -- Nonlinear activation functions; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2017.11.011
• Languages: English
• ISSNs: 0893-6080

Abstract

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.