Journal ArticleDOI
A recurrent neural network for solving Sylvester equation with time-varying coefficients
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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.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.read more
Citations
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Proceedings ArticleDOI
Zhang Dynamics and Gradient Dynamics with Tracking-Control Application
TL;DR: This paper shows the Zhang dynamics method, which was originally designed for constant problems solving, is generalized for time-varying linear equations solving and is exploited together to solve the tracking-control problem of a nonlinear system as a new application.
Book ChapterDOI
Comparison on Gradient-Based Neural Dynamics and Zhang Neural Dynamics for Online Solution of Nonlinear Equations
Yunong Zhang,Chenfu Yi,Weimu Ma +2 more
TL;DR: Computer-simulation results via power-sigmoid activation functions substantiate further the theoretical analysis and efficacy of Zhang neural dynamics on nonlinear equations solving.
Zhang neural network for lineartime-varyingequation solvingand itsroboticapplication
TL;DR: Zhang et al. as discussed by the authors proposed a recurrent neural network for time-varying equation solving, which is designed based on a variable-valued error function, instead of a constant value error function.
Journal ArticleDOI
Robustness analysis of the Zhang neural network for online time-varying quadratic optimization
TL;DR: Both theoretical-analysis and computer-simulation results demonstrate the good ZNN robustness and superior performance for online time-varying QM and QP problem solving, especially when using power-sigmoid activation functions.
Journal ArticleDOI
Discontinuous Neural Networks for Finite-Time Solution of Time-Dependent Linear Equations
TL;DR: The tightness of the estimated threshold is discussed and key differences in the role played by this threshold with respect to networks for solving time-invariant ALEs are pointed out.
References
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Book
Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
Book ChapterDOI
Output regulation of nonlinear systems
TL;DR: In this paper, the problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed.
Journal ArticleDOI
Nonlinear control via approximate input-output linearization: the ball and beam example
TL;DR: In this paper, an approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied, and a method for constructing approximate systems that are input output linearizable is provided.
Journal ArticleDOI
Pole assignment via Sylvester's equation
TL;DR: In this article, it was shown that the pole assignment problem can be reduced to solving the linear matrix equations AX − XA = −BG, FX = G successively for X, and then F for almost any choice of G.
Journal ArticleDOI
Neural networks for solving systems of linear equations and related problems
Andrzej Cichocki,Rolf Unbehauen +1 more
TL;DR: Various circuit architectures of simple neuron-like analog processors are considered for online solving of a system of linear equations with real constant and/or time-variable coefficients and can be used for solving linear and quadratic programming problems.
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