×

Finite-time synchronization of memristor neural networks via interval matrix method. (English) Zbl 1471.93240

Summary: In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.

MSC:

93D40 Finite-time stability
93B70 Networked control
93C43 Delay control/observation systems
93B52 Feedback control
93C10 Nonlinear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abdurahman, A.; Jiang, H.; Teng, Z., Finite-time synchronization for memristor-based neural networks with time-varying delays, Neural Networks, 69, 20-28 (2015) · Zbl 1398.34107
[2] Aubin, J. P.; Cellina, A., Differential inclusions: set-valued maps and viability theory: Vol. 264 (2012), Springer Science & Business Media
[3] Borghetti, J.; Snider, G. S.; Kuekes, P. J.; Yang, J. J.; Stewart, D.; Williams, R. S., ‘memristive’ switches enable ‘stateful’ logic operations via material implication, Nature, 464, 873-876 (2010)
[4] Chen, G.; Wei, F.; Wang, W., Finite-time stabilization for stochastic interval systems with time delay and application to energy-storing electrical circuits, Electronics, 8, 175 (2019)
[5] Chen, J.; Zeng, Z.; Jiang, P., Global mittag-leffler stability and synchronization of memristor-based fractional-order neural networks, Neural Networks, 51, 1-8 (2014) · Zbl 1306.34006
[6] Chen, C.; Zhu, S.; Wei, Y.; Yang, C., Finite-time stability of delayed memristor-based fractional-order neural networks, IEEE Transactions on Cybernetics (2018)
[7] Chua, L. O., Memristor-the missing circuit element, IEEE Transactions on Circuit Theory, 18, 507-519 (1971)
[8] Dorato, P., Short-time stability in linear time-varying systems, Proceedings of IRE International Convention Record (1961)
[9] Fan, Y.; Huang, X.; Li, Y.; Xia, J.; Chen, G., Aperiodically intermittent control for quasi-synchronization of delayed memristive neural networks: An interval matrix and matrix measure combined method, Systems Man and Cybernetics, 49, 2254-2265 (2019)
[10] Filippov, A. F., Differential equations with discontinuous right-hand side, Matematicheskii sbornik, 93, 99-128 (1960) · Zbl 0138.32204
[11] Gao, J.; Zhu, P.; Alsaedi, A.; Alsaadi, F. E.; Hayat, T., A new switching control for finite-time synchronization of memristor-based recurrent neural networks, Neural Networks, 86, 1-9 (2017) · Zbl 1429.93319
[12] Jiang, M.; Wang, S.; Mei, J.; Shen, Y., Finite-time synchronization control of a class of memristor-based recurrent neural networks, Neural Networks, 63, 133-140 (2015) · Zbl 1323.93007
[13] Koronovskii, A. A.; Moskalenko, O. I.; Hramov, A. E., On the use of chaotic synchronization for secure communication, Physics-Uspekhi, 52, 1213-1238 (2009)
[14] Li, Z.; Liu, H.; Lu, J.; Zeng, Z.; Lu, J., Synchronization regions of discrete-time dynamical networks with impulsive couplings, Information Sciences, 459, 265-277 (2018) · Zbl 1448.93253
[15] Liu, D.; Zhu, S.; Sun, K., Anti-synchronization of complex-valued memristor-based delayed neural networks, Neural Networks, 105, 1-13 (2018) · Zbl 1441.93280
[16] Lu, H., Chaotic attractors in delayed neural networks, Physics Letters. A, 298, 109-116 (2002) · Zbl 0995.92004
[17] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Physical Review Letters, 64, 821-824 (1990) · Zbl 0938.37019
[18] Shi, Y.; Zhu, P., Finite-time synchronization of stochastic memristor-based delayed neural networks, Neural Computing and Applications, 29, 293-301 (2018)
[19] Strukov, D. B.; Snider, G. S.; Stewart, D.; Williams, R. S., The missing memristor found, Nature, 453, 80-83 (2008)
[20] Su, L.; Zhou, L., Exponential synchronization of memristor-based recurrent neural networks with multi-proportional delays, Neural Computing and Applications, 31, 7907-7920 (2019)
[21] Sun, B.; Wen, S.; Wang, S.; Huang, T.; Chen, Y.; Li, P., Quantized synchronization of memristive neural networks with time-varying delays via super-twisting algorithm, Neurocomputing (2019), URL http://www.sciencedirect.com/science/article/pii/S0925231219315607
[22] Sun, K.; Zhu, S.; Wei, Y.; Zhang, X.; Gao, F., Finite-time synchronization of memristor-based complex-valued neural networks with time delays, Physics Letters. A, 383, 2255-2263 (2019) · Zbl 1475.93100
[23] Tour, J. M.; He, T., Electronics: The fourth element, Nature, 453, 42-43 (2008)
[24] Velmurugan, G.; Rakkiyappan, R.; Cao, J., Finite-time synchronization of fractional-order memristor-based neural networks with time delays, Neural Networks, 73, 36-46 (2016) · Zbl 1398.34110
[25] Wang, L.; Zeng, Z.; Ge, M.; Hu, J., Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays, Neural Networks, 105, 65-74 (2018) · Zbl 1441.93255
[26] Wen, S.; Bao, G.; Zeng, Z.; Chen, Y.; Huang, T., Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays, Neural Networks, 48, 195-203 (2013) · Zbl 1305.34129
[27] Wen, S.; Zeng, Z.; Chen, M. Z.Q.; Huang, T., Synchronization of switched neural networks with communication delays via the event-triggered control, IEEE Transactions on Neural Networks, 28, 2334-2343 (2017)
[28] Williams, R., How we found the missing memristor, IEEE Spectrum, 45, 28-35 (2008)
[29] Wu, M.; He, Y.; She, J. H., Stability analysis and robust control of time-delay systems: Vol. 22 (2010), Springer · Zbl 1250.93005
[30] Wu, A.; Wen, S.; Zeng, Z., Synchronization control of a class of memristor-based recurrent neural networks, Information Sciences, 183, 106-116 (2012) · Zbl 1243.93049
[31] Xia, J.; Chen, G.; Sun, W., Extended dissipative analysis of generalized markovian switching neural networks with two delay components, Neurocomputing, 260, 275-283 (2017)
[32] Xia, J.; Zhang, J.; Feng, J.; Wang, Z.; Zhuang, G., Command filter-based adaptive fuzzy control for nonlinear systems with unknown control directions, IEEE Transactions on Systems, Man, and Cybernetics: Systems (2019)
[33] Xia, J.; Zhang, J.; Sun, W.; Zhang, B.; Wang, Z., Finite-time adaptive fuzzy control for nonlinear systems with full state constraints, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49, 1541-1548 (2018)
[34] Xiao, Q.; Zeng, Z., Scale-limited lagrange stability and finite-time synchronization for memristive recurrent neural networks on time scales, IEEE Transactions on Systems, Man, and Cybernetics, 47, 2984-2994 (2017)
[35] Xu, Y.; Wang, H.; Li, Y.; Pei, B., Image encryption based on synchronization of fractional chaotic systems, Communications in Nonlinear Science and Numerical Simulation, 19, 3735-3744 (2014) · Zbl 1470.94099
[36] Yang, X.; Cao, J.; Liang, J., Exponential synchronization of memristive neural networks with delays: Interval matrix method, IEEE Transactions on Neural Networks, 28, 1878-1888 (2017)
[37] Yang, X.; Cao, J.; Yu, W., Exponential synchronization of memristive cohen-grossberg neural networks with mixed delays, Cognitive Neurodynamics, 8, 239-249 (2014)
[38] Yang, L.; Zeng, Z.; Shi, X., A memristor-based neural network circuit with synchronous weight adjustment, Neurocomputing, 363, 114-124 (2019)
[39] Zhang, G.; Shen, Y.; Yin, Q.; Sun, J., Passivity analysis for memristor-based recurrent neural networks with discrete and distributed delays, Neural Networks, 61, 49-58 (2015) · Zbl 1323.93018
[40] Zhang, H.; Sheng, Y.; Zeng, Z., Synchronization of coupled reaction-diffusion neural networks with directed topology via an adaptive approach, IEEE Transactions on Neural Networks, 29, 1550-1561 (2018)
[41] Zhang, H.; Zeng, Z.; Han, Q., Synchronization of multiple reaction-diffusion neural networks with heterogeneous and unbounded time-varying delays, IEEE Transactions on Systems, Man, and Cybernetics, 49, 2980-2991 (2019)
[42] Zhu, S.; Liu, D.; Yang, C.; Fu, J., Synchronization of memristive complex-valued neural networks with time delays via pinning control method, IEEE Transactions on Cybernetics (2019)
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.