Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion

IEEE Transactions on Neural Networks and Learning Systems

Volumn 25, Issue 2, 2014, Pages 370-382

  Guo, Dongsheng ^a   Zhang, Yunong ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Conversion; linear matrix inequality (LMI); theoretical analysis; time varying; zhang neural network (ZNN)

Indexed keywords

EXPLICIT DYNAMICS; MATRIX EQUATIONS; NEURAL DYNAMICS; THEORETICAL ANALYSIS; TIME VARYING; TIME-VARYING COEFFICIENT; ZHANG NEURAL NETWORK (ZNN); ZHANG NEURAL NETWORKS;

COMPUTER SIMULATION; RECURRENT NEURAL NETWORKS; SHIP CONVERSION; ZINC COMPOUNDS;

LINEAR MATRIX INEQUALITIES;

ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; COMPUTER SIMULATION; HUMAN; NERVE CELL; ONLINE SYSTEM; STATISTICAL MODEL;

COMPUTER SIMULATION; HUMANS; LINEAR MODELS; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NEURONS; ONLINE SYSTEMS;

EID: 84893672379     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2275011     Document Type: Article

References (35)

1. Z. Wang, H. Zhang, and B. Jiang, "LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures," IEEE Trans. Neural Netw., vol. 22, no. 7, pp. 1032-1045, Jul. 2011.
2. X. Li and J. Shen, "LMI approach for stationary oscillation of interval neural networks with discrete and distributed time-varying delays under impulsive perturbations," IEEE Trans. Neural Netw., vol. 21, no. 10, pp. 1555-1563, Oct. 2010.
3. J. Liang, Z. Wang, Y. Liu, and X. Liu, "Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks," IEEE Trans. Neural Netw., vol. 19, no. 11, pp. 1910-1921, Nov. 2008.
4. V. Singh, "A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 223-225, Jan. 2004.
5. E. Kim, H.-J. Kang, and M. Park, "Numerical stability analysis of fuzzy control systems via quadratic programming and linear matrix inequalities," IEEE Trans. Syst., Man, Cybern., A, Syst. Humans, vol. 29, no. 4, pp. 333-346, Jul. 1999.
6. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Solving quadratic distance problems: An LMI-based approach," IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 200-212, Feb. 2003.
7. M. Zhong, S. X. Ding, J. Lam, and H. Wang, "An LMI approach to design robust fault detection filter for uncertain LTI systems," Automatica, vol. 39, no. 3, pp. 543-550, Mar. 2003.
8. M. Liu, "Optimal exponential synchronization of general chaotic delayed neural networks: An LMI approach," Neural Netw., vol. 22, no. 7, pp. 949-957, Sep. 2009.
9. G. Chesi, "LMI techniques for optimization over polynomials in control: A survey," IEEE Trans. Autom. Control, vol. 55, no. 11, pp. 2500-2510, Nov. 2010.
10. X. Jing, "Robust adaptive learning of feedforward neural networks via LMI optimizations," Neural Netw., vol. 31, pp. 33-45, Jul. 2012.
11. C.-L. Lin, C.-C. Lai, and T.-H. Huang, "A neural network for linear matrix inequality problems," IEEE Trans. Neural Netw., vol. 11, no. 5, pp. 1078-1092, Sep. 2000.
12. L. Cheng, Z.-G. Hou, and M. Tan, "A simplified neural network for linear matrix inequality problems," Neural Process. Lett., vol. 29, no. 3, pp. 213-230, Jun. 2009.
13. X. Liao, G. Chen, and E. N. Sanchez, "Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach," Neural Netw., vol. 15, no. 7, pp. 855-866, 2002. (Pubitemid 35299581)
14. B. D. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods. Englewood Cliffs, NJ, USA: Prentice-Hall, 1990.
15. A. Megretski, "Necessary and sufficient conditions of stability: A multiloop generalization of the circle criterion," IEEE Trans. Autom. Control, vol. 38, no. 5, pp. 753-756, May 1993. (Pubitemid 23706277)
16. D. Guo and Y. Zhang, "A new variant of Zhang neural network for solving online time-varying linear inequalities," Proc. R. Soc. A, vol. 468, no. 2144, pp. 2255-2271, Aug. 2012.
17. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, MATLAB LMI Control Toolbox. Natick, MA, USA: The MathWorks Inc., 1995.
18. Z. Zhang and Y. Zhang, "Variable joint-velocity limits of redundant robot manipulators handled by quadratic programming," IEEE/ASME Trans. Mech., vol. 18, no. 2, pp. 674-686, Apr. 2013.
19. D. Guo and Y. Zhang, "A new inequality-based obstacle-avoidance MVN scheme and its application to redundant robot manipulators," IEEE Trans. Syst., Man, Cybern., C, Appl. Rev., vol. 42, no. 6, pp. 1326-1340, Nov. 2012.
20. Y. Zhang, D. Jiang, and J. Wang, "A recurrent neural network for solving Sylvester equation with time-varying coefficients," IEEE Trans. Neural Netw., vol. 13, no. 5, pp. 1053-1063, Sep. 2002.
21. Y. Zhang and S. S. Ge, "Design and analysis of a general recurrent neural network model for time-varying matrix inversion," IEEE Trans. Neural Netw., vol. 16, no. 6, pp. 1477-1490, Nov. 2005. (Pubitemid 41709645)
22. D. Guo, C. Yi, and Y. Zhang, "Zhang neural network versus gradientbased neural network for time-varying linear matrix equation solving," Neurocomputing, vol. 74, no. 17, pp. 3708-3712, Oct. 2011.
23. Y. Zhang and C. Yi, Zhang Neural Networks and Neural-Dynamic Method. Commack, NY, USA: Nova, 2011.
24. L. Xiao and Y. Zhang, "Zhang neural network versus gradient neural network for solving time-varying linear inequalities," IEEE Trans. Neural Netw., vol. 22, no. 10, pp. 1676-1684, Oct. 2011.
25. L. Xiao and Y. Zhang, "Two new types of Zhang neural networks solving systems of time-varying nonlinear inequalities," IEEE Trans. Circuits Syst. I, Regular Papers, vol. 59, no. 10, pp. 2363-2373, Oct. 2012.
26. F. Ding and T. Chen, "Gradient based iterative algorithms for solving a class of matrix equations," IEEE Trans. Autom. Control, vol. 50, no. 8, pp. 1216-1221, Aug. 2005. (Pubitemid 41410122)
27. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1991.
28. Y. Tassa and T. Erez, "Least squares solutions of the HJB equation with neural network value-function approximators," IEEE Trans. Neural Netw., vol. 18, no. 4, pp. 1031-1041, Jul. 2007. (Pubitemid 47098879)
29. L. V. Ferreira, E. Kaszkurewicz, and A. Bhaya, "Solving systems of linear equations via gradient systems with discontinuous righthand sides: Application to LS-SVM," IEEE Trans. Neural Netw., vol. 16, no. 2, pp. 501-505, Mar. 2005. (Pubitemid 40390834)
30. Q. Liu, J. Cao, and Y. Xia, "A delayed neural network for solving linear projection equations and its analysis," IEEE Trans. Neural Netw., vol. 16, no. 4, pp. 834-843, Jul. 2005. (Pubitemid 41064315)
31. C. Mead, Analog VLSI and Neural Systems. Reading, MA, USA: Addison-Wesley, 1989.
32. A. Ben-Israel and T. N. Greville, Generalized Inverses: Theory and Applications. New York, NY, USA: Springer-Verlag, 2003.
33. M. A. Rakha, "On the Moore-Penrose generalized inverse matrix," Appl. Math. Comput., vol. 158, no. 1, pp. 185-200, Oct. 2004.
34. Y. Zhang, Y. Yang, N. Tan, and B. Cai, "Zhang neural network solving for time-varying full-rank matrix Moore-Penrose inverse," Computing, vol. 92, no. 2, pp. 97-121, Jun. 2011.
35. J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, 4th ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 2004.