Analog VLSI and neural systems
Analog VLSI and neural systems
A Systolic Architecture for Fast Dense Matrix Inversion
IEEE Transactions on Computers
A recurrent neural network for real-time matrix inversion
Applied Mathematics and Computation
Dynamic inversion of nonlinear maps with applications to nonlinear control and robotics
Dynamic inversion of nonlinear maps with applications to nonlinear control and robotics
Digital Signal Processing
From Zhang neural network to Newton iteration for matrix inversion
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Expert Systems with Applications: An International Journal
Regularized image reconstruction using SVD and a neural networkmethod for matrix inversion
IEEE Transactions on Signal Processing
A recurrent neural network for solving Sylvester equation with time-varying coefficients
IEEE Transactions on Neural Networks
Design and analysis of a general recurrent neural network model for time-varying matrix inversion
IEEE Transactions on Neural Networks
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In this paper, we present, develop and investigate a special kind of recurrent neural network termed Zhang neural network (ZNN) for time-varying matrix inversion. Comparing with the dynamic system proposed by Getz and Marsden (G-M) for time-varying matrix inversion, we show that such a G-M dynamic system depicted in an explicit dynamics can also be derived from the presented ZNN model depicted in an implicit dynamics. In other words, a novel result on the relationship between the ZNN model and others' model/method (i.e., the G-M dynamic system) is found for time-varying matrix inversion. In addition, we propose and investigate the discrete-time algorithms (depicted by systems of difference equations) of the aforementioned ZNN and G-M models in two situations, i.e., the time-derivative of the time-varying matrix to be inverted being known or unknown. Simulative and numerical results demonstrate the superior performance of the ZNN models for time-varying matrix inversion, as well as the efficacy of the G-M dynamic system (which has to be started with initial conditions sufficiently close to the desired initial inverse). Furthermore, the ZNN models and G-M dynamic system are applied to the kinematic control of a two-link planar manipulator via online solution of time-varying matrix inversion.