Abstract
To obtain the online solution of complex-valued systems of linear equation in complex domain with higher precision and higher convergence rate, a new neural network based on Zhang neural network (ZNN) is investigated in this paper. First, this new neural network for complex-valued systems of linear equation in complex domain is proposed and theoretically proved to be convergent within finite time. Then, the illustrative results show that the new neural network model has the higher precision and the higher convergence rate, as compared with the gradient neural network (GNN) model and the ZNN model. Finally, the application for controlling the robot using the proposed method for the complex-valued systems of linear equation is realized, and the simulation results verify the effectiveness and superiorness of the new neural network for the complex-valued systems of linear equation.
Highlights
Today, the complex-valued systems of linear equation has been applied into many fields (DuranDiaz et al, 2011; Guo et al, 2011; Subramanian et al, 2014; Hezari et al, 2016; Zhang et al, 2016; Xiao et al, 2017a)
The application of the new design method for the complex-valued system of linear equation in robot domain has not been reported. This is the first time to propose a new neural network, which can convergence within finite-time for solving the complex-valued system of linear equation and its application to robot domain
Theoretical analyses and simulative results are presented to show the effectiveness of the proposed finite-time recurrent neural network
Summary
The complex-valued systems of linear equation has been applied into many fields (DuranDiaz et al, 2011; Guo et al, 2011; Subramanian et al, 2014; Hezari et al, 2016; Zhang et al, 2016; Xiao et al, 2017a). Xiao et al (2015) proposed a fully complex-valued gradient neural network (GNN) to solve such a complex-valued systems of linear equation. Xiao (2016) presented a new design formula, which can converge to 0 within finite time for the time-varying matrix inversion. Considering that a complex variable can be written as the combination of its real and imaginary parts, we have A = Are + jAim, b√= bre + jbim, and z(t) = zre(t) + zim(t), where the symbol j =. Where Are ∈ Rn×n, Aim ∈ Rn×n, zre ∈ Rn, zim ∈ Rn, bre ∈ Rn, and bim ∈ Rn. According to the complex formula, the real (or imaginary) part of the left-side and right-side of equation is equal (Zhang et al, 2016).
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