×

Exponential stabilization and synchronization for fuzzy model of memristive neural networks by periodically intermittent control. (English) Zbl 1415.93220

Summary: The problem of exponential stabilization and synchronization for fuzzy model of memristive neural networks (MNNs) is investigated by using periodically intermittent control in this paper. Based on the knowledge of memristor and recurrent neural network, the model of MNNs is formulated. Some novel and useful stabilization criteria and synchronization conditions are then derived by using the Lyapunov functional and differential inequality techniques. It is worth noting that the methods used in this paper are also applied to fuzzy model for complex networks and general neural networks. Numerical simulations are also provided to verify the effectiveness of theoretical results.

MSC:

93D20 Asymptotic stability in control theory
93C42 Fuzzy control/observation systems
68T05 Learning and adaptive systems in artificial intelligence
Full Text: DOI

References:

[1] Ali, M. S., Stability analysis of Markovian jumping stochastic Cohen Grossberg neural networks with discrete and distributed time varying delays, Chinese Physics B, 23, 6, 060702 (2014)
[2] Ali, M. S., Stability of Markovian jumping recurrent neural networks with discrete and distributed time-varying delays, Neurocomputing, 149, 1280-1285 (2015)
[3] Ali, M. S.; Arik, S.; Saravanakumar, R., Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays, Neurocomputing, 158, 167-173 (2015)
[4] Bainov, D.; Simeoov, P., Integral inequalities and applications (1992), Springer Science & Business Media · Zbl 0759.26012
[5] Boccaletti, S.; Latora, V.; Moreno, Y., Complex networks: structure and dynamics, Physics Reports, 424, 175 (2006) · Zbl 1371.82002
[6] Cai, S.; Hao, J.; Liu, Z., Exponential synchronization of chaotic systems with time-varying delays and parameter mismatches via intermittent control, Chaos: An Interdisciplinary Journal of Nonlinear Science, 21, 2, 023112 (2011) · Zbl 1317.34085
[7] Chandrasekar, A.; Rakkiyappan, R., Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks, Neurocomputing (2015)
[8] Chandrasekar, A.; Rakkiyappan, R.; Cao, J., Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach, Neural Networks, 70, 27-38 (2015) · Zbl 1396.93108
[9] Chandrasekar, A.; Rakkiyappan, R.; Cao, J., Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach, Neural Networks, 57, 79-93 (2014) · Zbl 1323.93032
[10] Chua, L. O., Memristor-the missing circuit element, IEEE Transactions on Circuit Theory, 18, 5, 507-519 (1971)
[11] Fang, Y.; Chow, T. W.S., Nonlinear dynamical systems control using a new RNN temporal learning strategy, IEEE Transactions on Circuits and Systems II: Express Briefs, 52, 11, 719-723 (2005)
[12] Halanay, A., Differential equations: stability, oscillations, time lags (1966), Academic Press · Zbl 0144.08701
[13] Hu, C.; Yu, J.; Jiang, H., Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control, Nonlinearity, 23, 10, 2369 (2010) · Zbl 1197.92005
[14] Hu, C.; Yu, J.; Jiang, H., Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control, Chaos: An Interdisciplinary Journal of Nonlinear Science, 20, 2, 023108 (2010) · Zbl 1311.92017
[15] Huang, T. W.; Li, C. D., Chaotic synchronization by the intermittent feedback method, Journal of Computational and Applied Mathematics, 234, 4, 1097-1104 (2010) · Zbl 1195.65212
[16] Li, X., Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects, Neurocomputing, 73, 4, 749-758 (2010)
[17] Li, X.; Ding, C.; Zhu, Q., Synchronization of stochastic perturbed chaotic neural networks with mixed delays, Journal of the Franklin Institute, 347, 7, 1266-1280 (2010) · Zbl 1202.93057
[18] Li, C. D.; Feng, G.; Liao, X. F., Stabilization of nonlinear systems via periodically intermittent control, IEEE Transactions on Circuits and Systems II: Express Briefs, 54, 11, 1019-1023 (2007)
[19] Li, C. D.; Liao, X. F.; Huang, T. W., Exponential stabilization of chaotic systems with delay by periodically intermittent control, Chaos: An Interdisciplinary Journal of Nonlinear Science, 17, 1, 013103 (2007) · Zbl 1159.93353
[20] Li, C.; Liao, X.; Yang, X., Switch control for piecewise affine chaotic systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 16, 3, 033104 (2006) · Zbl 1146.37327
[21] Li, C. D.; Liao, X. F.; Yang, X. F., Impulsive stabilization and synchronization of a class of chaotic delay systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 15, 4, 043103 (2005) · Zbl 1144.37371
[22] Li, C. D.; Liao, X., Impulsive effects on stability of high-order BAM neural networks with time delays, Neurocomputing, 74, 10, 1541-1550 (2011)
[23] Li, X.; O’Regan, D.; Akca, H., Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays, IMA Journal of Applied Mathematics, 80, 1, 85-99 (2015) · Zbl 1316.34079
[24] Li, X.; Rakkiyappan, R., Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays, Communications in Nonlinear Science and Numerical Simulation, 18, 6, 1515-1523 (2013) · Zbl 1286.34106
[25] Li, X.; Rakkiyappan, R., Stability results for Takagi-Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term, Neural Computing and Applications, 22, 1, 203-219 (2013)
[26] Li, X.; Song, S., Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays, IEEE Transactions on Neural Networks and Learning Systems, 24, 6, 868-877 (2013)
[27] Li, C. D.; Yu, W.; Huang, T. W., Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach, Neural Networks, 54, 85-94 (2014) · Zbl 1307.93377
[28] Liu, C.; Li, C.; Han, Q., Reachability and controllability of linear switched impulsive systems, IET Control Theory & Applications, 7, 9, 1294-1299 (2013)
[29] Sanchez, E. N.; Perez, J. P., Input-to-state stability (ISS) analysis for dynamic neural networks, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46, 11, 1395-1398 (1999) · Zbl 0956.68133
[30] Stamova, I.; Stamov, T.; Li, X., Global exponential stability of a class of impulsive cellular neural networks with supremums, International Journal of Adaptive Control and Signal Processing, 28, 11, 1227-1239 (2014) · Zbl 1338.93316
[31] Strogatz, S. H., Exploring complex networks, Nature, 410, 6825, 268-276 (2001) · Zbl 1370.90052
[32] Strukov, D. B.; Snider, G. S.; Stewart, D. R., The missing memristor found, Nature, 453, 7191, 80-83 (2008)
[33] Suykens, J. A.K.; Osipov, G. V., Introduction to focus issue: synchronization in complex networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 18, 3, 037101 (2008)
[34] Wada, N.; Saito, K.; Saeki, M., Model predictive control for linear parameter varying systems using parameter dependent Lyapunov function, IEEE transactions on Circuits and Systems II-Express Briefs, 53, 12, 1446-1450 (2004)
[35] Wen, S.; Huang, T.; Zeng, Z., Circuit design and exponential stabilization of memristive neural networks, Neural Networks, 63, 48-56 (2015) · Zbl 1323.93065
[36] Wen, S. P.; Zeng, Z. G.; Huang, T. W., Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays, Neurocomputing, 97, 233-240 (2012)
[37] Wen, S. P.; Zeng, Z. G.; Huang, T. W., Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators, IEEE Transactions on Fuzzy Systems, 22, 6, 1704-1713 (2014)
[38] Wu, A.; Zeng, Z., Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays, Neural Networks, 36, 1-10 (2012) · Zbl 1258.34165
[39] Wu, A.; Zeng, Z., Exponential stabilization of memristive neural networks with time delays, IEEE Transactions on Neural Networks and Learning Systems, 23, 12, 1919-1929 (2012)
[40] Wu, A.; Zeng, Z., Anti-synchronization control of a class of memristive recurrent neural networks, Communications in Nonlinear Science and Numerical Simulation, 18, 2, 373-385 (2013) · Zbl 1279.94157
[41] Wu, A.; Zeng, Z.; Zhu, X., Exponential synchronization of memristor-based recurrent neural networks with time delays, Neurocomputing, 74, 17, 3043-3050 (2011)
[42] Wu, A.; Zhang, J.; Zeng, Z., Dynamic behaviors of a class of memristor-based Hopfield networks, Physics Letters A, 375, 15, 1661-1665 (2011) · Zbl 1242.82035
[43] Wen, S. P.; Zeng, Z. G.; Huang, T. W., Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays, International Journal of Robust and Nonlinear Control, 25, 4, 610-624 (2015) · Zbl 1312.93098
[44] Xia, W.; Cao, J., Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos: An Interdisciplinary Journal of Nonlinear Science, 19, 1, 013120 (2009) · Zbl 1311.93061
[45] Yang, T., Impulsive control theory (2001), Springer Science & Business Media · Zbl 0996.93003
[46] Yue, D.; Han, Q. L.; Peng, C., State feedback controller design of networked control systems, (2004 proceedings of the 2004 IEEE international conference on control applications, Vol. 1 (2004), IEEE), 242-247
[47] Zhang, W.; Huang, J.; Wei, P., Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control, Applied Mathematical Modelling, 35, 2, 612-620 (2011) · Zbl 1205.93125
[48] Zhang, Wei; Li, Chuandong; Huang, Tingwen; He, Xing, Synchronization of memristor-based coupling recurrent neural networks with time-varying delays and impulses, IEEE Transactions on Neural Networks and Learning Systems, 26, 3308-3313 (2015)
[49] Zhang, G. D.; Shen, Y., Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control, Neural Networks, 55, 1-10 (2014) · Zbl 1322.93055
[50] Zhang, G. D.; Shen, Y.; Sun, J., Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays, Neurocomputing, 97, 149-154 (2012)
[51] Zhu, Q.; Zhang, T.; Fei, S., Adaptive neural control for a class of output feedback time delay nonlinear systems, Neurocomputing, 72, 7, 1985-1992 (2009)
[52] Żochowski, M., Intermittent dynamical control, Physica D: Nonlinear Phenomena, 145, 3, 181-190 (2000) · Zbl 0963.34030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.