Journal ArticleDOI
A recurrent neural network for solving Sylvester equation with time-varying coefficients
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TLDR
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
Improved finite-time zeroing neural network for time-varying division
TL;DR: A novel complex varying‐parameter finite‐time zeroing neural network for finding a solution to the time‐dependent division problem is introduced and an application of the introduced VPFTZNN model in an output tracking control time‐varying linear system is demonstrated.
Journal ArticleDOI
Distributed observer-based cooperative control for output regulation in multi-agent linear parameter-varying systems
TL;DR: The proposed solution method, the agents are divided into two groups depending on whether or not their output is directly affected by external inputs, and the solution to a time-varying Sylvester equation is proposed.
Journal ArticleDOI
Multi-dimensional Capon spectral estimation using discrete Zhang neural networks
TL;DR: This paper derives a novel implementation of a very computationally demanding matched filter-bank based a spectral estimator, namely the multi-dimensional Capon spectral estimators, and proposes to use the discrete Zhang neural network for the online covariance matrix inversion.
Journal ArticleDOI
The construction of high order convergent look-ahead finite difference formulas for Zhang Neural Networks
TL;DR: Zhang neural networks rely on convergent 1-step ahead finite difference formulas of which very few are known as discussed by the authors, and those which are known have been constructed in ad-hoc ways and suffer from low performance.
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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