Journal ArticleDOI
Discrete-time ZD, GD and NI for solving nonlinear time-varying equations
TLDR
Numerical examples and results demonstrate the efficacy and superiority of the proposed DTZD models for solving nonlinear time-varying equations, as compared with the DTGD model and NI.Abstract:
A special class of neural dynamics called Zhang dynamics (ZD), which is different from gradient dynamics (GD), has recently been proposed, generalized, and investigated for solving time-varying problems by following Zhang et al.'s design method. In view of potential digital hardware implemetation, discrete-time ZD (DTZD) models are proposed and investigated in this paper for solving nonlinear time-varying equations in the form of $f(x,t)=0$ . For comparative purposes, the discrete-time GD (DTGD) model and Newton iteration (NI) are also presented for solving such nonlinear time-varying equations. Numerical examples and results demonstrate the efficacy and superiority of the proposed DTZD models for solving nonlinear time-varying equations, as compared with the DTGD model and NI.read more
Citations
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Journal ArticleDOI
A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function
TL;DR: A robust and fixed-time zeroing neural dynamics model is proposed and analyzed for time-variant nonlinear equation (TVNE), and comparative results demonstrate the effectiveness, robustness, and advantage of the RaFT-ZND model for solving TVNE.
Journal ArticleDOI
Continuous and discrete Zhang dynamics for real-time varying nonlinear optimization
Long Jin,Yunong Zhang +1 more
TL;DR: Simulation and numerical results further illustrate the efficacy and advantages of the proposed CTZD and DTZD models for RTVNO.
Journal ArticleDOI
Solving Time-Varying System of Nonlinear Equations by Finite-Time Recurrent Neural Networks With Application to Motion Tracking of Robot Manipulators
Lin Xiao,Zhijun Zhang,Shuai Li +2 more
TL;DR: Computer simulations based on a numerical example validate the preponderance of the proposed FTRNNs for time-varying SoNE, as compared to the recently proposed Zhang neural network and its improved version.
Journal ArticleDOI
A nonlinearly activated neural dynamics and its finite-time solution to time-varying nonlinear equation
TL;DR: Simulations are performed to evaluate the performance of the proposed neural dynamics, which substantiate the effectiveness and superiority of the finite-time convergent neural dynamics for solving time-varying nonlinear equations in real time, as compared with the conventional gradient-based neural dynamics and the recently proposed Zhang neural dynamics.
Journal ArticleDOI
Theoretical analysis, numerical verification and geometrical representation of new three-step DTZD algorithm for time-varying nonlinear equations solving
TL;DR: Comparative numerical results further substantiate the efficacy and superiority of the proposed three-stepDTZD algorithm for solving time-varying nonlinear equations, as compared with the one-step DTZD algorithms.
References
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Analog VLSI and Neural Systems
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Design and analysis of a general recurrent neural network model for time-varying matrix inversion
Yunong Zhang,Shuzhi Sam Ge +1 more
TL;DR: Simulation results substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.
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A recurrent neural network for solving Sylvester equation with time-varying coefficients
TL;DR: 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.
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Numerical Methods using MATLAB
TL;DR: A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied.
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Design and analysis of a general recurrent neural network model for time-varying matrix inversion
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