Peng-Type ZNN Model Attempted for Online Diagonalization of Time-Varying Symmetric Matrix

Matrix diagonalization (or termed, matrix eigen-decomposition) is a vital part of matrix theory. Different from static matrix diagonalization problem, in this paper, the more challenging problem, i.e., time-varying symmetric matrix diagonalization problem, is mainly researched. For solving this problem, the ZNN (i.e., Zhang neural network) design method is employed, which has been formally proposed for finding online solutions of various time-varying problems. Besides, the try-and-error method is adopted to simplify an intermediate model. Then, an effective model termed Peng-type ZNN model is proposed and discussed. In order to verify the validity of the proposed model, three examples are considered. Simulation results illustrate that the steady-state errors are limited to a relatively small level, and the steady-state errors can be controlled by changing the diagonal matrix in the model. Therefore, the effectiveness of the proposed Peng-type ZNN model is testified.

[1]  Dogan Ibrahim.  Advanced PIC Microcontroller Projects in C: From USB to RTOS with the PIC 18F Series , 2008 .

[2]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[3]  D. Bianco,et al.  Matrix diagonalization algorithm and its applicability to the nuclear shell model , 2011 .

[4]  George Lindfield,et al.  Numerical Methods Using MATLAB , 1998 .

[5]  Q. Cheng,et al.  Estimates for eigenvalues on Riemannian manifolds , 2009 .

[6]  Julián Fernández Bonder,et al.  Precise asymptotic of eigenvalues of resonant quasilinear systems , 2008, 0811.1542.

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

[8]  John B. Peatman,et al.  Design with PIC microcontrollers , 1988 .

[9]  Chris Nagy.  Embedded Systems Design Using the TI Msp430 Series: Embedded Technology , 2003 .

[10]  Abhishek K Gupta,et al.  Numerical Methods using MATLAB , 2014, Apress.

[11]  Hsiao-Chun Wu,et al.  Robust Blind Beamforming Algorithm Using Joint Multiple Matrix Diagonalization , 2005, IEEE Sensors Journal.

[12]  G. Fasano.  Lanczos Conjugate-Gradient Method and Pseudoinverse Computation on Indefinite and Singular Systems , 2007 .

[13]  M. Rotter,et al.  Dynamical matrix diagonalization for the calculation of dispersive excitations , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[14]  Shuai Li,et al.  A New Varying-Parameter Convergent-Differential Neural-Network for Solving Time-Varying Convex QP Problem Constrained by Linear-Equality , 2018, IEEE Transactions on Automatic Control.

[15]  Uwe Helmke,et al.  Diagonalization of Time Varying Symmetric Matrices , 2002, International Conference on Computational Science.

[16]  S. R. Searle,et al.  On the history of the kronecker product , 1983 .

[17]  Yunong Zhang,et al.  Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints , 2009 .

[18]  Hitoshi Iba,et al.  Reconstruction of Gene Regulatory Networks from Gene Expression Data Using Decoupled Recurrent Neural Network Model , 2013 .

[19]  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.

[20]  Feng Ding,et al.  On the Kronecker Products and Their Applications , 2013, J. Appl. Math..

[21]  Yunong Zhang,et al.  Comparison on Gradient-Based Neural Dynamics and Zhang Neural Dynamics for Online Solution of Nonlinear Equations , 2008, ISICA.

[22]  Zhigang Zeng,et al.  Analysis and design of associative memories based on recurrent neural network with discontinuous activation functions , 2012, Neurocomputing.