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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Journal ArticleDOI
Different Zhang functions resulting in different ZNN models demonstrated via time-varying linear matrix-vector inequalities solving
Lin Xiao,Yunong Zhang +1 more
TL;DR: This paper puts research emphasis on the ZNN-3 model for solving time-varying linear matrix-vector inequalities (including its design process, theoretical analysis and simulation verification), which possesses the property of superior convergence and better accuracy.
Journal ArticleDOI
Novel Recurrent Neural Network for Time-Varying Problems Solving [Research Frontier]
Dongsheng Guo,Yunong Zhang +1 more
TL;DR: The artificial neural-dynamic approach based on RNN has been viewed as a powerful alternative to online solution of mathematical problems arising in numerous fields of science and engineering, such as matrix inversion in robots redundancy resolution and pseudoinversetype solution.
Journal ArticleDOI
Robustness analysis of a hybrid of recursive neural dynamics for online matrix inversion
TL;DR: Theoretical analysis shows that the perturbed dynamic system is still global stable with the tight steady-state bound of solution error estimated, and global exponential convergence rate and finite convergence time of such a hybrid dynamical model to a relatively loose solution error bound are analyzed.
Journal ArticleDOI
Comparison on neural solvers for the Lyapunov matrix equation with stationary & nonstationary coefficients
Chenfu Yi,Yuhuan Chen,Xinhua Lan +2 more
TL;DR: Computer simulation results show that, when used to solve the whether stationary or nonstationary problems, the convergence performance of ZNN solvers are superior than that of GNNsolvers.
Journal ArticleDOI
Bounded Z-type neurodynamics with limited-time convergence and noise tolerance for calculating time-dependent Lyapunov equation
TL;DR: A unified design formula for the ZND is proposed by combining the nonlinear activation function and the integral term, and a bounded ZND (BZND) model is proposed and used to compute a real-time-dependent Lyapunov equation in noisy environments.
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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