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

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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

Abstract
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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 and 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), 635-641. doi: 10.1016/S0005-1098(96)00180-X.
[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), 416-429. doi: 10.1109/TRO.2008.915438.
[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), 867-880. doi: 10.3934/jimo.2009.5.867.
[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), 471-475.
[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), 817-826.
[6]	X. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay, Physical Review E, 68 (2003), 1-7. doi: 10.1103/PhysRevE.68.016118.
[7]	X. Y. Lou and B. T. Cui, Passivity analysis of integro-differential neural networks with time-varying delays, Neurocomputing, 70 (2007), 1071-1078.
[8]	R. Lozano, B. Brogliato, O. Egeland and B. Maschke, "Systems Analysis and Control: Theory and Applications, Dissipative," Springer-Verlag, London, U.K., 2000.
[9]	M. S. Mahmoud and A. Ismail, Passivity and passification of time-delay systems, Journal of Mathematical Analysis and Applications, 292 (2004), 247-258. doi: 10.1016/j.jmaa.2003.11.055.
[10]	J. H. Park, Further results on passivity analysis of delayed cellular neural networks, Chaos, Solitons and Fractals, 34 (2007), 1546-1551. doi: 10.1016/j.chaos.2005.04.124.
[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), 515-526. doi: 10.1016/j.jprocont.2007.07.007.
[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), 161-165. doi: 10.1109/TCSII.2006.886464.
[13]	H. Santoso, J. Bao and P. L. Lee, Dynamic operability analysis for stable and unstable linear processes, Industrial & Engineering Chemistry Research, 47 (2008), 4765-4774. doi: 10.1021/ie070599c.
[14]	S. Wang, Q. Shao and X. Zhou, Knot-optimizing spline networks (KOSNETS) for nonparametric regression, Journal of Industrial and Management Optimization, 4 (2008), 33-52.
[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), 389-404.
[16]	Y. Yatsenko and N. Hritonenko, Optimization of the lifetime of capital equipment using integral models, Journal of Industrial and Management Optimization, 1 (2005), 415-432.
[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), 256-259. doi: 10.1109/81.904893.
[18]	W. Yu and X. Li, New results on system identification with dynamic neural networks, IEEE Transactions on Neural Networks, 12 (2001), 412-417. doi: 10.1109/72.914535.
[19]	W. Yu, Passivity analysis for dynamic multilayer neuro identifier, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173-178.

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), 635-641. doi: 10.1016/S0005-1098(96)00180-X.
[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), 416-429. doi: 10.1109/TRO.2008.915438.
[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), 867-880. doi: 10.3934/jimo.2009.5.867.
[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), 471-475.
[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), 817-826.
[6]	X. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay, Physical Review E, 68 (2003), 1-7. doi: 10.1103/PhysRevE.68.016118.
[7]	X. Y. Lou and B. T. Cui, Passivity analysis of integro-differential neural networks with time-varying delays, Neurocomputing, 70 (2007), 1071-1078.
[8]	R. Lozano, B. Brogliato, O. Egeland and B. Maschke, "Systems Analysis and Control: Theory and Applications, Dissipative," Springer-Verlag, London, U.K., 2000.
[9]	M. S. Mahmoud and A. Ismail, Passivity and passification of time-delay systems, Journal of Mathematical Analysis and Applications, 292 (2004), 247-258. doi: 10.1016/j.jmaa.2003.11.055.
[10]	J. H. Park, Further results on passivity analysis of delayed cellular neural networks, Chaos, Solitons and Fractals, 34 (2007), 1546-1551. doi: 10.1016/j.chaos.2005.04.124.
[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), 515-526. doi: 10.1016/j.jprocont.2007.07.007.
[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), 161-165. doi: 10.1109/TCSII.2006.886464.
[13]	H. Santoso, J. Bao and P. L. Lee, Dynamic operability analysis for stable and unstable linear processes, Industrial & Engineering Chemistry Research, 47 (2008), 4765-4774. doi: 10.1021/ie070599c.
[14]	S. Wang, Q. Shao and X. Zhou, Knot-optimizing spline networks (KOSNETS) for nonparametric regression, Journal of Industrial and Management Optimization, 4 (2008), 33-52.
[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), 389-404.
[16]	Y. Yatsenko and N. Hritonenko, Optimization of the lifetime of capital equipment using integral models, Journal of Industrial and Management Optimization, 1 (2005), 415-432.
[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), 256-259. doi: 10.1109/81.904893.
[18]	W. Yu and X. Li, New results on system identification with dynamic neural networks, IEEE Transactions on Neural Networks, 12 (2001), 412-417. doi: 10.1109/72.914535.
[19]	W. Yu, Passivity analysis for dynamic multilayer neuro identifier, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (2003), 173-178.

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