American Institute of Mathematical Sciences

Advanced
April  2011, 7(2): 283-289. doi: 10.3934/jimo.2011.7.283

New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays

Zhigang Zeng 1, and  Tingwen Huang 2,

1. 

Department of Control Science & Engineering, Huazhong University of Science & Technology, and Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, Hubei 430074, China
2. 

Texas A&M University at Qatar, Doha, P.O. Box 5825, Qatar, United States

Received  December 2009 Revised  September 2010 Published  April 2011

In this paper, by using some analytic techniques, several sufficient conditions are given to ensure the passivity of continuous-time recurrent neural networks with delays. The passivity conditions are presented in terms of some negative semi-definite matrices. They are easily verifiable and easier to check computing with some conditions in terms of complicated linear matrix inequality.
Keywords: Passivity, linear matrix inequality., neural networks, negative semi-definite matrix, delays.
Mathematics Subject Classification: Primary: 34A25, 34A34; Secondary: 15A2.
Citation: Zhigang Zeng, Tingwen Huang. New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays. Journal of Industrial & Management Optimization, 2011, 7 (2) : 283-289. doi: 10.3934/jimo.2011.7.283
References:
[1]

S. Commuri and F. L. Lewis, CMAC neural networks for control of nonlinear dynamical systems: structure, stability and passivity,, Automatica, 33 (1996), 635.  doi: 10.1016/S0005-1098(96)00180-X.  Google Scholar

[2]

A. Kugi, C. Ott, A. Albu-Schaffer and G. Hirzinger, On the passivity-based impedance control of flexible joint robots,, IEEE Transactions on Robotics, 24 (2008), 416.  doi: 10.1109/TRO.2008.915438.  Google Scholar

[3]

J. Li, H. R. Feng and M.C. Wang, A replenishment policy with defective products, backlog and delay of payments,, Journal of Industrial and Management Optimization, 5 (2009), 867.  doi: 10.3934/jimo.2009.5.867.  Google Scholar

[4]

C. G. Li and X. F. Liao, Passivity analysis of neural networks with time delay,, IEEE Transactions on Circuits and Systems-II: Express Briefs, 52 (2005), 471.   Google Scholar

[5]

L. Lin, D. He and Z. Y. Tan, Bounds on delay start lpt algorithm for scheduling on two identical machines in the l(p) norm,, Journal of Industrial and Management Optimization, 4 (2008), 817.   Google Scholar

[6]

X. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay,, Physical Review E, 68 (2003), 1.  doi: 10.1103/PhysRevE.68.016118.  Google Scholar

[7]

X. Y. Lou and B. T. Cui, Passivity analysis of integro-differential neural networks with time-varying delays,, Neurocomputing, 70 (2007), 1071.   Google Scholar

[8]

R. Lozano, B. Brogliato, O. Egeland and B. Maschke, "Systems Analysis and Control: Theory and Applications, Dissipative,", Springer-Verlag, (2000).   Google Scholar

[9]

M. S. Mahmoud and A. Ismail, Passivity and passification of time-delay systems,, Journal of Mathematical Analysis and Applications, 292 (2004), 247.  doi: 10.1016/j.jmaa.2003.11.055.  Google Scholar

[10]

J. H. Park, Further results on passivity analysis of delayed cellular neural networks,, Chaos, 34 (2007), 1546.  doi: 10.1016/j.chaos.2005.04.124.  Google Scholar

[11]

O. J. Rojas, J. Bao and P. L. Lee, On dissipativity, passivity and dynamic operability of nonlinear processes,, Journal of Process Control, 18 (2008), 515.  doi: 10.1016/j.jprocont.2007.07.007.  Google Scholar

[12]

J. J. Rubio and W. Yu, Stability analysis of nonlinear system identification via delayed neural networks,, IEEE Transactions on Circuits and Systems-II: Express Briefs, 54 (2007), 161.  doi: 10.1109/TCSII.2006.886464.  Google Scholar

[13]

H. Santoso, J. Bao and P. L. Lee, Dynamic operability analysis for stable and unstable linear processes,, Industrial & Engineering Chemistry Research, 47 (2008), 4765.  doi: 10.1021/ie070599c.  Google Scholar

[14]

S. Wang, Q. Shao and X. Zhou, Knot-optimizing spline networks (KOSNETS) for nonparametric regression,, Journal of Industrial and Management Optimization, 4 (2008), 33.   Google Scholar

[15]

L. X. Xu and W. Q. Liu, A new recurrent neural network adaptive approach for host-gate way rate control protocol within intranets using ATM ABR service,, Journal of Industrial and Management Optimization, 1 (2005), 389.   Google Scholar

[16]

Y. Yatsenko and N. Hritonenko, Optimization of the lifetime of capital equipment using integral models,, Journal of Industrial and Management Optimization, 1 (2005), 415.   Google Scholar

[17]

W. Yu and X. Li, Some stability properties of dynamic neural networks,, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 48 (2001), 256.  doi: 10.1109/81.904893.  Google Scholar

[18]

W. Yu and X. Li, New results on system identification with dynamic neural networks,, IEEE Transactions on Neural Networks, 12 (2001), 412.  doi: 10.1109/72.914535.  Google Scholar

[19]

W. Yu, Passivity analysis for dynamic multilayer neuro identifier,, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173.   Google Scholar

show all references

References:
[1]

S. Commuri and F. L. Lewis, CMAC neural networks for control of nonlinear dynamical systems: structure, stability and passivity,, Automatica, 33 (1996), 635.  doi: 10.1016/S0005-1098(96)00180-X.  Google Scholar

[2]

A. Kugi, C. Ott, A. Albu-Schaffer and G. Hirzinger, On the passivity-based impedance control of flexible joint robots,, IEEE Transactions on Robotics, 24 (2008), 416.  doi: 10.1109/TRO.2008.915438.  Google Scholar

[3]

J. Li, H. R. Feng and M.C. Wang, A replenishment policy with defective products, backlog and delay of payments,, Journal of Industrial and Management Optimization, 5 (2009), 867.  doi: 10.3934/jimo.2009.5.867.  Google Scholar

[4]

C. G. Li and X. F. Liao, Passivity analysis of neural networks with time delay,, IEEE Transactions on Circuits and Systems-II: Express Briefs, 52 (2005), 471.   Google Scholar

[5]

L. Lin, D. He and Z. Y. Tan, Bounds on delay start lpt algorithm for scheduling on two identical machines in the l(p) norm,, Journal of Industrial and Management Optimization, 4 (2008), 817.   Google Scholar

[6]

X. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay,, Physical Review E, 68 (2003), 1.  doi: 10.1103/PhysRevE.68.016118.  Google Scholar

[7]

X. Y. Lou and B. T. Cui, Passivity analysis of integro-differential neural networks with time-varying delays,, Neurocomputing, 70 (2007), 1071.   Google Scholar

[8]

R. Lozano, B. Brogliato, O. Egeland and B. Maschke, "Systems Analysis and Control: Theory and Applications, Dissipative,", Springer-Verlag, (2000).   Google Scholar

[9]

M. S. Mahmoud and A. Ismail, Passivity and passification of time-delay systems,, Journal of Mathematical Analysis and Applications, 292 (2004), 247.  doi: 10.1016/j.jmaa.2003.11.055.  Google Scholar

[10]

J. H. Park, Further results on passivity analysis of delayed cellular neural networks,, Chaos, 34 (2007), 1546.  doi: 10.1016/j.chaos.2005.04.124.  Google Scholar

[11]

O. J. Rojas, J. Bao and P. L. Lee, On dissipativity, passivity and dynamic operability of nonlinear processes,, Journal of Process Control, 18 (2008), 515.  doi: 10.1016/j.jprocont.2007.07.007.  Google Scholar

[12]

J. J. Rubio and W. Yu, Stability analysis of nonlinear system identification via delayed neural networks,, IEEE Transactions on Circuits and Systems-II: Express Briefs, 54 (2007), 161.  doi: 10.1109/TCSII.2006.886464.  Google Scholar

[13]

H. Santoso, J. Bao and P. L. Lee, Dynamic operability analysis for stable and unstable linear processes,, Industrial & Engineering Chemistry Research, 47 (2008), 4765.  doi: 10.1021/ie070599c.  Google Scholar

[14]

S. Wang, Q. Shao and X. Zhou, Knot-optimizing spline networks (KOSNETS) for nonparametric regression,, Journal of Industrial and Management Optimization, 4 (2008), 33.   Google Scholar

[15]

L. X. Xu and W. Q. Liu, A new recurrent neural network adaptive approach for host-gate way rate control protocol within intranets using ATM ABR service,, Journal of Industrial and Management Optimization, 1 (2005), 389.   Google Scholar

[16]

Y. Yatsenko and N. Hritonenko, Optimization of the lifetime of capital equipment using integral models,, Journal of Industrial and Management Optimization, 1 (2005), 415.   Google Scholar

[17]

W. Yu and X. Li, Some stability properties of dynamic neural networks,, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 48 (2001), 256.  doi: 10.1109/81.904893.  Google Scholar

[18]

W. Yu and X. Li, New results on system identification with dynamic neural networks,, IEEE Transactions on Neural Networks, 12 (2001), 412.  doi: 10.1109/72.914535.  Google Scholar

[19]

W. Yu, Passivity analysis for dynamic multilayer neuro identifier,, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173.   Google Scholar

[1]

Yi Xu, Jinjie Liu, Liqun Qi. A new class of positive semi-definite tensors. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-11. doi: 10.3934/jimo.2018186
[2]

Sihem Guerarra. Positive and negative definite submatrices in an Hermitian least rank solution of the matrix equation AXA*=B. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 15-22. doi: 10.3934/naco.2019002
[3]

Lipu Zhang, Yinghong Xu, Zhengjing Jin. An efficient algorithm for convex quadratic semi-definite optimization. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 129-144. doi: 10.3934/naco.2012.2.129
[4]

Xiantao Xiao, Liwei Zhang, Jianzhong Zhang. On convergence of augmented Lagrangian method for inverse semi-definite quadratic programming problems. Journal of Industrial & Management Optimization, 2009, 5 (2) : 319-339. doi: 10.3934/jimo.2009.5.319
[5]

Yue Lu, Ying-En Ge, Li-Wei Zhang. An alternating direction method for solving a class of inverse semi-definite quadratic programming problems. Journal of Industrial & Management Optimization, 2016, 12 (1) : 317-336. doi: 10.3934/jimo.2016.12.317
[6]

Wei Huang, Ka-Fai Cedric Yiu, Henry Y. K. Lau. Semi-definite programming based approaches for real-time tractor localization in port container terminals. Numerical Algebra, Control & Optimization, 2013, 3 (4) : 665-680. doi: 10.3934/naco.2013.3.665
[7]

Monika Eisenmann, Etienne Emmrich, Volker Mehrmann. Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data. Evolution Equations & Control Theory, 2019, 8 (2) : 315-342. doi: 10.3934/eect.2019017
[8]

Stephane Chretien, Paul Clarkson. A fast algorithm for the semi-definite relaxation of the state estimation problem in power grids. Journal of Industrial & Management Optimization, 2020, 16 (1) : 431-443. doi: 10.3934/jimo.2018161
[9]

Yuhong Dai, Nobuo Yamashita. Convergence analysis of sparse quasi-Newton updates with positive definite matrix completion for two-dimensional functions. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 61-69. doi: 10.3934/naco.2011.1.61
[10]

Jui-Pin Tseng. Global asymptotic dynamics of a class of nonlinearly coupled neural networks with delays. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4693-4729. doi: 10.3934/dcds.2013.33.4693
[11]

Tingting Su, Xinsong Yang. Finite-time synchronization of competitive neural networks with mixed delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3655-3667. doi: 10.3934/dcdsb.2016115
[12]

Cheng-Hsiung Hsu, Suh-Yuh Yang. Traveling wave solutions in cellular neural networks with multiple time delays. Conference Publications, 2005, 2005 (Special) : 410-419. doi: 10.3934/proc.2005.2005.410
[13]

Fernando Hernando, Diego Ruano. New linear codes from matrix-product codes with polynomial units. Advances in Mathematics of Communications, 2010, 4 (3) : 363-367. doi: 10.3934/amc.2010.4.363
[14]

Jiang-Xia Nan, Deng-Feng Li. Linear programming technique for solving interval-valued constraint matrix games. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1059-1070. doi: 10.3934/jimo.2014.10.1059
[15]

Daniel Alpay, Eduard Tsekanovskiĭ. Subclasses of Herglotz-Nevanlinna matrix-valued functtons and linear systems. Conference Publications, 2001, 2001 (Special) : 1-13. doi: 10.3934/proc.2001.2001.1
[16]

Ruoxia Li, Huaiqin Wu, Xiaowei Zhang, Rong Yao. Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation. Mathematical Control & Related Fields, 2015, 5 (4) : 827-844. doi: 10.3934/mcrf.2015.5.827
[17]

Paul Skerritt, Cornelia Vizman. Dual pairs for matrix groups. Journal of Geometric Mechanics, 2019, 11 (2) : 255-275. doi: 10.3934/jgm.2019014
[18]

Meijuan Shang, Yanan Liu, Lingchen Kong, Xianchao Xiu, Ying Yang. Nonconvex mixed matrix minimization. Mathematical Foundations of Computing, 2019, 2 (2) : 107-126. doi: 10.3934/mfc.2019009
[19]

Adel Alahmadi, Hamed Alsulami, S.K. Jain, Efim Zelmanov. On matrix wreath products of algebras. Electronic Research Announcements, 2017, 24: 78-86. doi: 10.3934/era.2017.24.009
[20]

Behrouz Kheirfam. Multi-parametric sensitivity analysis of the constraint matrix in piecewise linear fractional programming. Journal of Industrial & Management Optimization, 2010, 6 (2) : 347-361. doi: 10.3934/jimo.2010.6.347

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences