MATLAB Simulink Modeling and Simulation of Zhang Neural Network for Online Time-Varying Matrix Inversion

Recently, a special kind of recurrent neural networks (RNN) with implicit dynamics has been proposed by Zhang et al for online time-varying problems solving (such as time-varying matrix inversion). Such a neural-dynamic system is elegantly designed by defining a matrix-valued error function rather than the usual scalar-valued norm-based error function. Its computational error can be made decrease to zero globally and exponentially. For the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, we investigate in this paper the MATLAB Simulink modeling and simulative verification of such a Zhang neural network (ZNN). By using click-and-drag mouse operations, it is easier to model and simulate in comparison with MATLAB coding. Both convergence and robustness properties of such a ZNN model are analyzed, which substantiate the effectiveness of Zhang neural network on inverting the time-varying matrices.

[1]  L.P. Caloba,et al.  A new algorithm for analog matrix inversion , 1995, 38th Midwest Symposium on Circuits and Systems. Proceedings.

[2]  Robert H. Sturges,et al.  Analog matrix inversion [robot kinematics] , 1988, IEEE J. Robotics Autom..

[3]  Michael A. Fiddy,et al.  Regularized image reconstruction using SVD and a neural network method for matrix inversion , 1993, IEEE Trans. Signal Process..

[4]  Yunong Zhang,et al.  O(N 2)-Operation Approximation of Covariance Matrix Inverse in Gaussian Process Regression Based on Quasi-Newton BFGS Method , 2007, Commun. Stat. Simul. Comput..

[5]  Jun Wang,et al.  A recurrent neural network for real-time matrix inversion , 1993 .

[6]  Yunong Zhang,et al.  Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[7]  Shuzhi Sam Ge,et al.  Design and analysis of a general recurrent neural network model for time-varying matrix inversion , 2005, IEEE Transactions on Neural Networks.

[8]  Yunong Zhang,et al.  Time-series Gaussian Process Regression Based on Toeplitz Computation of O(N2) Operations and O(N)-level Storage , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[9]  Yeung Yam,et al.  Complex recurrent neural network for computing the inverse and pseudo-inverse of the complex matrix , 1998, Appl. Math. Comput..

[10]  Yunong Zhang,et al.  Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process , 2005, Appl. Math. Comput..

[11]  Jun Wang,et al.  A recurrent neural network for solving Sylvester equation with time-varying coefficients , 2002, IEEE Trans. Neural Networks.

[12]  Tze-Fun Chan,et al.  Modelling of the three-phase induction motor using SIMULINK , 1997, 1997 IEEE International Electric Machines and Drives Conference Record.

[13]  Luo Fa-long,et al.  Neural network approach to computing matrix inversion , 1992 .

[14]  Yu-Nong Zhang,et al.  Zhang Neural Network for Linear Time-Varying Equation Solving and its Robotic Application , 2007, 2007 International Conference on Machine Learning and Cybernetics.

[15]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[16]  Soo-Young Lee,et al.  An Optimization Network for Matrix Inversion , 1987, NIPS.

[17]  S. Hakimi,et al.  Analog methods for computation of the generalized inverse , 1968 .