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Erschienen in: International Journal of Machine Learning and Cybernetics 2/2015

01.04.2015 | Original Article

State estimation for memristor-based neural networks with time-varying delays

verfasst von: Hongzhi Wei, Ruoxia Li, Chunrong Chen

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 2/2015

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Abstract

This paper is concerned with the state estimation problem for a class of memristor-based neural networks with time-varying delay. A delay dependent condition is developed to estimate the neuron states through observed output measurements such that the error system is globally asymptotically stable. By constructing more effective Lyapunov functionals, and combining with Jensen integral inequality and free-weighting matrix approach, a less conservative sufficient condition for the existence of state estimator is formulated in terms of linear matrix inequality, which can be checked efficiently by using some standard numerical packages. Finally, a numerical example is given to demonstrate the effectiveness of the presented results.

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Literatur
1.
Zurück zum Zitat Chua LO (1971) Memristor-the missing circut element. IEEE Trans Circuit Theory 18:507–519CrossRef Chua LO (1971) Memristor-the missing circut element. IEEE Trans Circuit Theory 18:507–519CrossRef
3.
Zurück zum Zitat Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453:80–83CrossRef Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453:80–83CrossRef
4.
Zurück zum Zitat Di Ventra M, Pershin YV, Chua LO (2009) Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc IEEE 97:1717–1724CrossRef Di Ventra M, Pershin YV, Chua LO (2009) Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc IEEE 97:1717–1724CrossRef
5.
Zurück zum Zitat Anthes G (2010) Memristor: passorfail, Commun ACM 54:22–24 Anthes G (2010) Memristor: passorfail, Commun ACM 54:22–24
6.
Zurück zum Zitat Rubio J, Yu W (2007) Nonlinear system identification with recurrent neural networks and dead-zone Kalman filter algorithm. Neurocomputing 70:2460–2466CrossRef Rubio J, Yu W (2007) Nonlinear system identification with recurrent neural networks and dead-zone Kalman filter algorithm. Neurocomputing 70:2460–2466CrossRef
7.
Zurück zum Zitat Li T, Fei S, Zhu Q, Cong S (2008) Exponential synchronization of chaotic neural networks with mixed delays. Neurocomputing 71:3005–3019CrossRef Li T, Fei S, Zhu Q, Cong S (2008) Exponential synchronization of chaotic neural networks with mixed delays. Neurocomputing 71:3005–3019CrossRef
8.
Zurück zum Zitat Li T, Song A, Fei S, Guo Y (2009) Synchronization control of chaotic neural networks with time-varying and distributed delays. Nonlinear Anal Theory Methods Appl 71:2372–2384 Li T, Song A, Fei S, Guo Y (2009) Synchronization control of chaotic neural networks with time-varying and distributed delays. Nonlinear Anal Theory Methods Appl 71:2372–2384
9.
Zurück zum Zitat Gan Q (2013) Synchronization of competitive neural networks with different time scales and time-varying delay based on delay partitioning approach. Int J Mach Learn Cybern 4:327–337CrossRef Gan Q (2013) Synchronization of competitive neural networks with different time scales and time-varying delay based on delay partitioning approach. Int J Mach Learn Cybern 4:327–337CrossRef
10.
Zurück zum Zitat Chen W, Lu X (2006) Delay-dependent exponential stability of neural networks with variable delay: an LMI approach, IEEE Trans. Circuits Syst II Exp Briefs 53:837–842CrossRef Chen W, Lu X (2006) Delay-dependent exponential stability of neural networks with variable delay: an LMI approach, IEEE Trans. Circuits Syst II Exp Briefs 53:837–842CrossRef
11.
Zurück zum Zitat Zheng C, Zhang Y, Wang Z (2014) Stability analysis of stochastic reaction-diffusion neural networks with Markovian switching and time delays in the leakage terms. Int J Mach Learn Cybern 5:3–12CrossRefMathSciNet Zheng C, Zhang Y, Wang Z (2014) Stability analysis of stochastic reaction-diffusion neural networks with Markovian switching and time delays in the leakage terms. Int J Mach Learn Cybern 5:3–12CrossRefMathSciNet
12.
Zurück zum Zitat Song Q, Wang Z (2008) Neural networks with discrete and distributed time-varying delays: a general stability analysis. Chaos Solitons Fractals 37:1538–1547CrossRefMATHMathSciNet Song Q, Wang Z (2008) Neural networks with discrete and distributed time-varying delays: a general stability analysis. Chaos Solitons Fractals 37:1538–1547CrossRefMATHMathSciNet
13.
Zurück zum Zitat Zhang H, Xie Y, Wang Z, Zheng C (2007) Adaptive synchronization between two different chaotic neural networks with timedelay. IEEE Trans Neural Netw 18:1841–1845CrossRef Zhang H, Xie Y, Wang Z, Zheng C (2007) Adaptive synchronization between two different chaotic neural networks with timedelay. IEEE Trans Neural Netw 18:1841–1845CrossRef
14.
Zurück zum Zitat Zhang H, Liu Z, Huang G (2010) Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via SC technique. IEEE Trans Syst Man Cybern B Cybern 40:1480–1491 Zhang H, Liu Z, Huang G (2010) Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via SC technique. IEEE Trans Syst Man Cybern B Cybern 40:1480–1491
15.
Zurück zum Zitat Syed Ali M (2014) Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays. Int J Mach Learn Cybern 5:13–22 Syed Ali M (2014) Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays. Int J Mach Learn Cybern 5:13–22
16.
Zurück zum Zitat Zhang H, Luo Y, Liu D (2009) Neural-network-based near-optimal control for a class of discrete-time affine nonlinear system swith control constraints. IEEE Trans Neural Netw 20:1490–1503CrossRef Zhang H, Luo Y, Liu D (2009) Neural-network-based near-optimal control for a class of discrete-time affine nonlinear system swith control constraints. IEEE Trans Neural Netw 20:1490–1503CrossRef
17.
Zurück zum Zitat Zhang H, Liu Z, Huang G, Wang Z (2010) Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans Neural Netw 21:91–106CrossRef Zhang H, Liu Z, Huang G, Wang Z (2010) Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans Neural Netw 21:91–106CrossRef
18.
Zurück zum Zitat Wang X, Dong C, Fan T (2007) Training T-S norm neural networks to refine weights for fuzzy if-then rules. Neurocomputing 70:2581–2587CrossRef Wang X, Dong C, Fan T (2007) Training T-S norm neural networks to refine weights for fuzzy if-then rules. Neurocomputing 70:2581–2587CrossRef
19.
Zurück zum Zitat Tsang ECC, Wang XZ, Yeung DS (2000) Improving learning accuracy of fuzzy decision trees by hybrid neural networks. IEEE Trans Fuzzy Syst 8:601–614 Tsang ECC, Wang XZ, Yeung DS (2000) Improving learning accuracy of fuzzy decision trees by hybrid neural networks. IEEE Trans Fuzzy Syst 8:601–614
20.
Zurück zum Zitat Elanayer VTS, Shin YC (1994) Approximation and estimation of nonlinear stochastic dynamic systems using radial function neural networks. IEEE Trans Neural Netw 5:594–603CrossRef Elanayer VTS, Shin YC (1994) Approximation and estimation of nonlinear stochastic dynamic systems using radial function neural networks. IEEE Trans Neural Netw 5:594–603CrossRef
21.
Zurück zum Zitat Huang H, Feng G, Cao J (2008) Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans Neural Netw 19:1329–1339CrossRef Huang H, Feng G, Cao J (2008) Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans Neural Netw 19:1329–1339CrossRef
22.
Zurück zum Zitat Park JH, Kwon OM (2009) Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl Math Comput 208:69–75CrossRefMATHMathSciNet Park JH, Kwon OM (2009) Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl Math Comput 208:69–75CrossRefMATHMathSciNet
23.
Zurück zum Zitat Park JH, Kwon OM, Lee SM (2008) State estimation for neural networks of neutral-type with interval time-varying delays. Appl Math Comput 203:217–223CrossRefMATHMathSciNet Park JH, Kwon OM, Lee SM (2008) State estimation for neural networks of neutral-type with interval time-varying delays. Appl Math Comput 203:217–223CrossRefMATHMathSciNet
24.
Zurück zum Zitat Lou X, Cui B (2008) Design of state estimator for uncertain neural networks via the integral-inequality method. Nonlinear Dyn 53:223–235CrossRefMATHMathSciNet Lou X, Cui B (2008) Design of state estimator for uncertain neural networks via the integral-inequality method. Nonlinear Dyn 53:223–235CrossRefMATHMathSciNet
25.
Zurück zum Zitat Liu Y, Wang Z, Liu X (2007) Design of exponential state estimators for neural networks with mixed time delays. Phys Lett A 364:401–412 Liu Y, Wang Z, Liu X (2007) Design of exponential state estimators for neural networks with mixed time delays. Phys Lett A 364:401–412
26.
Zurück zum Zitat Rakkiyappan R, Sakthivel N, Park JH, Kwon OM (2013) Sampled-data state estimation for Markovian jumping fuzzy cellular neural networks with mode-dependent probabilistic time-varying delays. Appl Math Comput 221:741–769CrossRefMathSciNet Rakkiyappan R, Sakthivel N, Park JH, Kwon OM (2013) Sampled-data state estimation for Markovian jumping fuzzy cellular neural networks with mode-dependent probabilistic time-varying delays. Appl Math Comput 221:741–769CrossRefMathSciNet
27.
Zurück zum Zitat Lee TH, Park JH, Kwon OM, Lee SM (2013) Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw 46:99–108CrossRefMATH Lee TH, Park JH, Kwon OM, Lee SM (2013) Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw 46:99–108CrossRefMATH
28.
Zurück zum Zitat Aubin J, Frankowska H (1990) Set-valued analysis. Birkhauser, BostonMATH Aubin J, Frankowska H (1990) Set-valued analysis. Birkhauser, BostonMATH
29.
Zurück zum Zitat Filippov A (1984) Differential equations with discontinuous right-hand side. In: Mathematics and Its Applications (Soviet Series). Kluwer Academic, Boston Filippov A (1984) Differential equations with discontinuous right-hand side. In: Mathematics and Its Applications (Soviet Series). Kluwer Academic, Boston
30.
Zurück zum Zitat Liao X, Chen G, Sanchez EN (2002) LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans Circuits Syst I 49:1033–1039CrossRefMathSciNet Liao X, Chen G, Sanchez EN (2002) LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans Circuits Syst I 49:1033–1039CrossRefMathSciNet
31.
Zurück zum Zitat Morita M (1993) Associative memory with nonmonotone dynamics. Neural Netw 6:115–126CrossRef Morita M (1993) Associative memory with nonmonotone dynamics. Neural Netw 6:115–126CrossRef
32.
Zurück zum Zitat Gu K, Kharitonov VL, Chen J (2003) Stability of Time-delay Systems. Birkhauser, MassachusettsCrossRefMATH Gu K, Kharitonov VL, Chen J (2003) Stability of Time-delay Systems. Birkhauser, MassachusettsCrossRefMATH
33.
Zurück zum Zitat Boyd S, Ghaoui LEI, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadephia Boyd S, Ghaoui LEI, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadephia
34.
Zurück zum Zitat Huang H, Feng G (2011) State estimation of recurrent neural networks with time-varying delay: a novel delay partition approach. Neurocomputing 74:792–796CrossRef Huang H, Feng G (2011) State estimation of recurrent neural networks with time-varying delay: a novel delay partition approach. Neurocomputing 74:792–796CrossRef
35.
Zurück zum Zitat Lakshmanan S, Park JH, Ji DH, Jung HY, Nagamani G (2012) State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. Nonlinear Dyn. 70:1421–1434CrossRefMATHMathSciNet Lakshmanan S, Park JH, Ji DH, Jung HY, Nagamani G (2012) State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. Nonlinear Dyn. 70:1421–1434CrossRefMATHMathSciNet
Metadaten
Titel
State estimation for memristor-based neural networks with time-varying delays
verfasst von
Hongzhi Wei
Ruoxia Li
Chunrong Chen
Publikationsdatum
01.04.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 2/2015
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-014-0257-x

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