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
Simulation and Comparison of Zhang Neural Network and Gradient Neural Network Solving for Time-Varying Matrix Square Roots
Yunong Zhang,Yiwen Yang +1 more
TL;DR: This paper develops, generalize, simulate and compare the ZNN and GNN models for online solution of time-varying matrix square roots, and results via power-sigmoid activation functions further substantiate the superior ZNN convergence in time-Varying problems solving as compared to the GNN model.
Journal ArticleDOI
General 7-Instant DCZNN Model Solving Future Different-Level System of Nonlinear Inequality and Linear Equation
TL;DR: Several comparative numerical experiments are provided to substantiate the efficacy and superiority of the general 7-instant ZeaD formula and the corresponding 7IDCZNN model for solving FDLSNILE.
Journal ArticleDOI
Different-level two-norm and infinity-norm minimization to remedy joint-torque instability/divergence for redundant robot manipulators
Dongsheng Guo,Yunong Zhang +1 more
TL;DR: Computer-simulation results based on the PUMA560 robot manipulator demonstrate the effectiveness and advantages of the proposed different-level bi-criteria minimization scheme for robotic redundancy resolution.
Journal ArticleDOI
A system of generalized Sylvester quaternion matrix equations and its applications
TL;DR: This paper derives some necessary and sufficient conditions for the solvability to the system of generalized Sylvester real quaternion matrix equations and gives an expression of the general solution to the above mentioned system.
Journal ArticleDOI
Superior performance of using hyperbolic sine activation functions in ZNN illustrated via time-varying matrix square roots finding
Yunong Zhang,Long Jin,Zhende Ke +2 more
TL;DR: Theoretical analysis and computer-simulation results demonstrate the superior performance of the ZNN model using hyperbolic sine activation functions in the context of large model-implementation errors, in comparison with that using linear activation functions.
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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