Convergence properties analysis of gradient neural network for solving online linear equations

Zidonghua Xuebao/ Acta Automatica Sinica

Volumn 35, Issue 8, 2009, Pages 1136-1139

  Zhang, Yu Nong ^a   Chen, Zeng Hai ^a   Chen, Ke ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Activation function array; Global exponential convergence; Gradient neural network (GNN)

Indexed keywords

ACTIVATION-FUNCTION ARRAY; CONVERGENCE PROPERTIES; GLOBAL EXPONENTIAL CONVERGENCE; GRADIENT NEURAL NETWORK (GNN); SIMULATION RESULT;

COMPUTER NETWORKS; NEURAL NETWORKS;

COMPUTER SIMULATION;

EID: 69849093201     PISSN: 02544156     EISSN: None     Source Type: Journal    
DOI: 10.3724/SP.J.1004.2009.01136     Document Type: Article

References (18)

1. Zhang Y N. Towards piecewise-linear primal neural networks for optimization and redundant robotics. In: Proceedings of IEEE International Conference on Networking, Sensing and Control. Fort Lauderdale, USA: IEEE, 2006. 374-379
2. Steriti R J, Fiddy M A. Regularized image reconstruction using SVD and a neural network method for matrix inversion. IEEE Transactions on Signal Processing, 1993, 41(10): 3074-3077
3. Sarkar T, Siarkiewicz K, Stratton R. Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems. IEEE Transactions on Antennas Propagation, 1981, 29(6): 847-856
4. Sturges R H J. Analog matrix inversion (robot kinematics). IEEE Journal of Robotics and Automation, 1988, 4(2): 157-162
5. 2) operations and O(N)-level storage. In: Proceedings of the 44th IEEE Conference on Decision and Control. Seville, Spain: IEEE, 2005. 3711-3716
6. 2)-operation approximation of covariance matrix inverse in Gaussian process regression based on quasi-Newton BFGS methods. Communications in Statistics-Simulation and Computation, 2007, 36(1-3): 367-380
7. Yu You-Li, Xu Li-Hong, Wu Qi-Di. Generalized fuzzy neural network. Acta Automatica Sinica, 2003, 29(6): 867-875
8. Manherz R K, Jordan B W, Hakimi S L. Analog methods for computation of the generalized inverse. IEEE Transactions on Automatic Control, 1968, 13(5): 582-585
9. Zhang Y N. Revisit the analog computer and gradient-based neural system for matrix inversion. In: Proceedings of IEEE International Symposium on Intelligent Control. Cyprus, the Republic of Cyprus: IEEE, 2005. 1411-1416
10. Zhang Y N, Jiang D, Wang J. A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Transactions on Neural Networks, 2002, 13(5): 1053-1063
11. Zhang Y N, Ge S S. Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Transactions on Neural Networks, 2005, 16(6): 1477-1490
12. Yang Hui, Chai Tian-You. Component content soft-sensor based on neural networks in rare-earth countercurrent extraction process. Acta Automatica Sinica, 2006, 32(4): 489-495
13. Wang J. Electronic realization of recurrent neural network for solving simultaneous linear equation. Electronics Letters, 1992, 28(5): 493-495
14. Zhang Y N, Wang J. Global exponential stability of recurrent neural network for synthesizing linear feedback control systems via pole assignment. IEEE Transactions on Neural Networks, 2002, 13(3): 633-644
15. Zhang Y N. A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network. Neurocomputing, 2006, 70(1-3): 513-524
16. Mead C. Analog VLSI and Neural Systems. Massachusetts: Addison-Wesley, 1989
17. Ferreira L V, Kaszkurewicz E, Bhaya A. Solving systems of linear equations via gradient systems with discontinuous right-hand sides: application to LS-SVM. IEEE Transactions on Neural Networks, 2005, 16(2): 501-505
18. Bhaya A, Kaszkurewicz E. A control-theoretic approach to the design of zero finding numerical methods. IEEE Transactions on Automatic Control, 2007, 52(6): 1014-1026