SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS

doi:10.1007/s10473-019-0116-7

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 195-213.doi: 10.1007/s10473-019-0116-7

SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS

M. SYED ALI¹, N. GUNASEKARAN^1,2, 曹进德³

1. Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu, India, 632 115, India;
2. Research Center for Wind Energy Systems, Kunsan National University, Kunsan, Chonbuk, 573-701, Korea;
3. School of Mathematics, Southeast University, Nanjing 210096, China

收稿日期:2017-09-07 修回日期:2017-12-14 出版日期:2019-02-25 发布日期:2019-11-14
通讯作者: M. SYED ALI E-mail:syedgru@gmail.com
作者简介:N. GUNASEKARAN,E-mail:gunasmaths@gmail.com;Jinde CAO,E-mail:jdcao@seu.edu.cn

SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS

M. SYED ALI¹, N. GUNASEKARAN^1,2, Jinde CAO³

1. Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu, India, 632 115, India;
2. Research Center for Wind Energy Systems, Kunsan National University, Kunsan, Chonbuk, 573-701, Korea;
3. School of Mathematics, Southeast University, Nanjing 210096, China

Received:2017-09-07 Revised:2017-12-14 Online:2019-02-25 Published:2019-11-14
Contact: M. SYED ALI E-mail:syedgru@gmail.com

摘要/Abstract

摘要： In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time-varying delay components via sampleddata control. By constructing a suitable Lyapunov-Krasovskii functional with triple and four integral terms and by using Jensen's inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

关键词: Lyapunov method, linear matrix inequality, state estimation, sample-data control, time-varying delays

Abstract: In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time-varying delay components via sampleddata control. By constructing a suitable Lyapunov-Krasovskii functional with triple and four integral terms and by using Jensen's inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

Key words: Lyapunov method, linear matrix inequality, state estimation, sample-data control, time-varying delays

M. SYED ALI, N. GUNASEKARAN, 曹进德. SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS[J]. 数学物理学报(英文版), 2019, 39(1): 195-213.

M. SYED ALI, N. GUNASEKARAN, Jinde CAO. SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS[J]. Acta mathematica scientia,Series B, 2019, 39(1): 195-213.

参考文献

[1] Tian J K, Zhong S M. Improved delay-dependent stability criterion for neural networks with time-varying delays. Appl Math Comput, 2011, 217:10278-10288
[2] Kwon O M, Lee S M, Park Ju H, Cha E J. New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput, 2012, 218:9953-9964
[3] Zhao Y, Gao H, Mou S. Asymptotic stability analysis of neural networks with successive time delay components. Neurocomputing, 2008, 71:2848-2856
[4] Arik S. An improved robust stability result for uncertain neural networks with multiple time delays. Neural Netw, 2014, 54:1-10
[5] Zeng H B, He Y, Wu M, Zhang C F. Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays. IEEE Trans Neural Netw, 2011, 22:806-812
[6] Gu K, Kharitonov V L, Chen J. Stability of Time Delay Systems. Boston:Birkhuser, 2003
[7] Liu Y, Lee S M, Kwon O M, Park J H. New approach to stability criteria for generalized neural networks with interval time-varying delays. Neurocomputing, 2015, 149:1544-1551
[8] Syed Ali M, Gunasekaran N, Zhu Quanxin. Stability analysis for neural networks with time-varying delay based on quadratic convex combination. Fuzzy Sets and Systems, 2017, 306:87-104
[9] Arbi A, Cao J, Alsaedi A. Improved synchronization analysis of competitive neural networks with timevarying delays. Nonlinear Analysis:Modelling and Control, 2018, 23:82-102
[10] Wang T, Qiu J, Gao H, Wang C. Network-based fuzzy control for nonlinear industrial processes with predictive compensation strategy. IEEE Trans SMC:Systems, 2017, 47:2137-2147
[11] Wang T, Qiu J, Yin S, Gao H, Fan J. Performance-based adaptive fuzzy tracking control for networked industrial processes. IEEE Trans Cybernetics, 2016, 46:1760-1770
[12] Zhang X, Li X, Cao J, Miaudi F. Design of delay-dependent controllers for finite-time stabilization of delayed neural networks with uncertainty. Journal of Franklin Institute, 2018, 355:5394-5413
[13] He Y, Liu G P, Rees D. Stability analysis for neural networks with time-varying interval delay. IEEE Trans Neural Netw, 2007, 18:1850-1854
[14] Song Q, Cao J D, Zhao Z. Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays. Nonlinear Anal Real World Appl, 2006, 7:65-80
[15] Zuo Z, Yang C, Wang Y. A new method for stability analysis of recurrent neural networks with interval time-varying delay. IEEE Trans Neural Netw, 2010, 21:339-344
[16] Shao H, Han Q L. New Delay-Dependent stability criteria for neural networks with two additive timevarying delay components. IEEE Trans Neural Netw, 2011, 22:812-818
[17] Ge X. Comments and an improved result on stability analysis for continuous system with additive time- varying delays:A less conservative results. Appl Math Comput, 2014, 241:42-46
[18] Liu Y, Lee S M, Lee H G. Robust delay-dependent stability criteria for uncertain neural networks with two additive time-varying delay components. Neurocomputing, 2015, 151:770-775
[19] Tian J, Zhong S. Improved delay-dependent stability criteria for neural networks with two additive timevarying delay components. Neurocomputing, 2012, 77:114-149
[20] Li X, Rakkiyappan R. Delay-dependent global asympotic stability criteria for stochastic genetic regulatory networks with Markovian jumping parameters. Applied Mathematical Modelling, 2012, 36:1718-1730
[21] Zhang H, Yang F, Liu X, Zhang Q. Stability analysis for neural networks with time-varying delay based on quadratic convex combination. IEEE Trans Neural Netw Learn Syst, 2013, 24:513-521
[22] Wang H, Song Q. State estimation for neural networks with mixed interval time-varying delays. Neurocomputing, 2010, 73:1281-1288
[23] Ren J, Zhu H, Zhong S, Ding Y, Shi K. State estimation for neural networks with multiple time delays. Neurocomputing, 2015, 151:501-510
[24] Bao H, Cao J. Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay. Neural Networks, 2011, 24(1):19-28
[25] Li N, Cao J. Switched exponential state estimation and robust stability for interval neural networks with the average dwell time. IMA Journal of Mathematical Control and Information, 2015, 32:257-276
[26] Huang H, Feng G, Cao J. Guaranteed performance state estimation of static neural networks with timevarying delay. Neurocomputing, 2011, 74:606-616
[27] Mahmoud M S. New exponentially convergent state estimation method for delayed neural networks. Neurocomputing, 2009, 72:3935-3942
[28] Huang H, Feng G, Cao J. An LMI approach to delay-dependent state estimation for delayed neural networks. Neurocomputing, 2011, 74:792-796
[29] Huang H, Feng G, Cao J. Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans Neural Netw, 2008, 19:1329-1339
[30] Wang Z, Ho D W C, Liu X. State estimation for delayed neural networks. IEEE Trans Neural Netw, 2005, 16:279-284
[31] Li T, Fei S M, Zhu Q. Design of exponential state estimator for neural networks with distributed delays. Nonlinear Anal Real World Appl, 2009, 10:1229-1242
[32] Park J H, Kwon O M. Further results on state estimation for neural networks of neutral-type with timevarying delay. Appl Math Comput, 2009, 208:69-75
[33] Lu J G, Hill D J. Global asymptotical synchronization of chaotic Lur'e systems using sampled data:A linear matrix inequality approach. IEEE Trans Circuits Syst-I, 2008, 55:586-590
[34] Zhang L, Gao H, Kaynak O. Network-induced constraints in networked control systems-a survey. IEEE Trans Ind Inf, 2013, 9:403-416
[35] Zhu X L, Wang Y. Stabilization for sampled-data neural-network-based control systems. IEEE Trans Syst Man Cybern-Part B:Cybern, 2011, 41:210-221
[36] Zhang W, Yu L. Stabilization of sampled-data control systems with control inputs missing. IEEE Trans Automat Control, 2010, 55:447-452
[37] Hu J, Li N, Liu X, Zhang G. Sampled-data state estimation for delayed neural networks with Markovian jumping parameters. Nonlinear Dyn, 2013, 73:275-284
[38] Lee T H, Park J H, Lee S M. Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw, 2013, 46:99-108
[39] Cao J, Sivasamy R, Rakkaiyappan R. Sampled-data H∞ synchronization of chaotic Lur'e systems with time delay. Circuits, Systems&Signal Processing, 2016, 35(3):811-835
[40] Rakkiyappan R, Sakthivel N, Cao J. Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Neural Networks, 2015, 66: 46-63
[41] Dharani S, Rakkaiyappan R, Cao J. Robust stochastic sampled-data H∞ control for a class of mechanical systems with uncertainties. ASME J Dyn Sys, Measurement and Control, 2015, 137(10):101008
[42] Theesar S, Banerjee S, Balasubramaniam P. Synchronization of chaotic systems under sampled-data control. Nonlinear Dyn, 2012, 70:1977-1987
[43] Zhang C, He Y, Wu M. Exponential synchronization of neural networks with time-varying mixed delays and sampled-data. Neurocomputing, 2010, 74:265-273
[44] Zhu X L, Wang Y. Stabilization for sampled-data neural-network-based control systems. IEEE Trans Syst Man Cybern-Part B:Cybern, 2011, 41:210-221
[45] Wu Z, Shi P, Su H, Chu J. Exponential stabilization for sampled-data neural-network-based control systems. IEEE Trans Neural Netw Learn Syst, 2014, 25:2180-2190
[46] Park P G, Ko J W, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47:235-238
[47] Kwon O M, Park M J, Park J H, Lee S M, Cha E J. Analysis on robust H∞ performance and stability for linear systems with interval time-varying state delays via some new augmented Lyapunov-Krasovskii functional. Appl Math Comput, 2013, 224:108-122
[48] Zhang H, Yang F, Liu X, Zhang Q. Stability analysis for neural networks with time-varying delay based on quadratic convex combination. IEEE Trans Neural Netw Learn Syst, 2013, 24:513-521

SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS

SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS

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