×

zbMATH — the first resource for mathematics

Finite-time stabilization control of memristor-based neural networks. (English) Zbl 1336.93135
Summary: This paper investigates the finite-time stabilization problem for a general class of Memristor-based Neural Networks (MNNs). Firstly, based on set-valued analysis and Kakutani’s fixed-point theorem of set-valued maps, the existence of equilibrium point can be guaranteed for MNNs. Then, by designing novel discontinuous controllers, some sufficient conditions are proposed to stabilize the states of such MNNs in finite time. Moreover, we give the upper bound of the settling time for stabilization which depends on the system parameters and control gains. The main tools to be used involve the framework of Filippov differential inclusions, non-smooth analysis, matrix theory and the famous finite-time stability theorem of nonlinear system. Finally, the theoretical results are verified by concrete examples with computer simulations.

MSC:
93D21 Adaptive or robust stabilization
92B20 Neural networks for/in biological studies, artificial life and related topics
47H10 Fixed-point theorems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chua, L. O., Memristor-the missing circuit element, IEEE Trans. Circuit Theory, CT-18, 507-519, (1971)
[2] Wu, A. L.; Zeng, Z. G., Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays, Neural Netw., 36, 1-10, (2012) · Zbl 1258.34165
[3] Wu, A. L.; Wen, S. P.; Zeng, Z. G., Synchronization control of a class of memristor-based recurrent neural networks, Inform. Sci., 183, 106-116, (2012) · Zbl 1243.93049
[4] Wu, A. L.; Zeng, Z. G., Exponential stabilization of memristive neural networks with time delays, IEEE Trans. Neural Netw. Learn. Syst., 23, 12, 1919-1929, (2012)
[5] Wu, A. L.; Zeng, Z. G., Anti-synchronization control of a class of memristive recurrent neural networks, Commun. Nonlinear Sci. Numer. Simul., 18, 373-385, (2013) · Zbl 1279.94157
[6] Zhang, G. D.; Shen, Y.; Yin, Q.; Sun, J. W., Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays, Inform. Sci., 232, 386-396, (2013) · Zbl 1293.34094
[7] Zhang, G. D.; Shen, Y.; Wang, L. M., Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays, Neural Netw., 46, 1-8, (2013) · Zbl 1296.93075
[8] Zhang, G. D.; Shen, Y., New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays, IEEE Trans. Neural Netw. Learn. Syst., 24, 10, 1701-1707, (2013)
[9] Guo, Z. Y.; Wang, J.; Yan, Z., Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays, Neural Netw., 48, 158-172, (2013) · Zbl 1297.93129
[10] Wen, S. P.; Bao, G.; Zeng, Z. G.; Chen, Y. R.; Huang, T. W., Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays, Neural Netw., 48, 195-203, (2013) · Zbl 1305.34129
[11] Yang, X.; Cao, J.; Yu, W. W., Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays, Cogn. Neurodynam., 8, 239-249, (2014)
[12] Cai, Z. W.; Huang, L. H., Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays, Commun. Nonlinear Sci. Numer. Simul., 19, 1279-1300, (2014)
[13] Chandrasekar, A.; Rakkiyappan, R.; Cao, J. D.; Lakshmanand, S., Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach, Neural Netw., 57, 79-93, (2014) · Zbl 1323.93032
[14] Jiang, M. H.; Wang, S. T.; Mei, J.; Shen, Y. J., Finite-time synchronization control of a class of memristor-based recurrent neural networks, Neural Netw., 63, 133-140, (2015) · Zbl 1323.93007
[15] Liu, X. Y.; Park, J. H.; Jiang, N.; Cao, J. D., Nonsmooth finite-time stabilization of neural networks with discontinuous activations, Neural Netw., 52, 25-32, (2014) · Zbl 1307.93353
[16] Liu, X. Y.; Ho, D. W.C.; Yu, W. W.; Cao, J. D., A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks, Neural Netw., 57, 94-102, (2014) · Zbl 1323.93064
[17] Aubin, J. P.; Cellina, A., Differential inclusions, (1984), Springer-Verlag Berlin
[18] Aubin, J. P.; Frankowska, H., Set-valued analysis, (1990), Birkhauser Boston, MA
[19] Filippov, A. F., (Differential Equations with Discontinuous Right-hand Side, Mathematics and Its Applications (Soviet Series), (1988), Kluwer Academic Boston)
[20] Blagodat-skik, V. I.; Filippov, A. F., Differential inclusions and optimal control, Proc. Steklov Inst. Math., 4, 199-259, (1986) · Zbl 0608.49027
[21] Clarke, F. H., Optimization and nonsmooth analysis, (1983), Wiley New York · Zbl 0727.90045
[22] Clarke, F. H.; Ledyaev, Y.; Stern, R. J.; Wolenski, P. R., Nonsmooth analysis and control theory, (1998), Springer-Verlag New York · Zbl 1047.49500
[23] Forti, M.; Grazzini, M.; Nistri, P.; Pancioni, L., Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations, Physica D, 214, 88-89, (2006) · Zbl 1103.34044
[24] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities, (1988), Cambridge University Press London · Zbl 0634.26008
[25] Guo, Z. Y.; Wang, J.; Yan, Z., Attractivity analysis of memristor-based cellular neural networks with time-varying delays, IEEE Trans. Neural Netw. Learn. Syst., 25, 4, 704-717, (2014)
[26] Wang, X.; Li, C. D.; Huang, T. W.; Duan, S. K., Global exponential stability of a class of memristive neural networks with time-varying delays, Neural Comput. Appl., 24, 7, 1707-1715, (2014)
[27] 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)
[28] Lu, J. Q.; Cao, J. D.; Ho, D. W.C., Adaptive stabilization and synchronization for chaotic lur’e systems with time-varying delay, IEEE Trans. Circuits Syst. I, 55, 5, 1347-1356, (2008)
[29] Li, L. L.; Ho, D. W.C.; Lu, J. Q., A unified approach to practical consensus with quantized data and time delay, IEEE Trans. Circuits Syst. I, 55, 5, 1347-1356, (2008)
[30] Cai, Z. W.; Huang, L. H.; Wang, D. S.; Zhang, L. L., Periodic synchronization in delayed memristive neural networks based on Filippov systems, J. Franklin Inst. B, 352, 4638-4663, (2015) · Zbl 1395.93273
[31] Lu, J. Q.; Cao, J. D., Adaptive synchronization of uncertain dynamical networks with delayed coupling, Nonlinear Dynam., 53, 1-2, 107-115, (2007) · Zbl 1182.92007
[32] Zhang, W. Y.; Xing, K. Y.; Li, J. M.; Chen, M. L., Adaptive synchronization of delayed reaction diffusion FCNNs via learning control approach, J. Intell. Fuzzy Systems, 28, 1, 141-150, (2015) · Zbl 1351.93088
[33] Zhang, W. Y., Stability analysis of Markovian jumping impulsive stochastic delayed RDCGNNs with partially known transition probabilities, Adv. Difference Equ., 2015, 102, (2015) · Zbl 1345.92018
[34] Zhang, W. Y.; Li, J. M., Global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays, Chin. Phys. B, 20, 3, (2011)
[35] Zhang, W. Y.; Li, J. M.; Chen, M. L., Dynamical behaviors of impulsive stochastic reaction-diffusion neural networks with mixed time delays, Abstr. Appl. Anal., (2012) · Zbl 1246.35108
[36] Li, J. M.; Zhang, W. Y.; Chen, M. L., Synchronization of delayed reaction-diffusion neural networks via an adaptive learning control approach, Comput. Math. Appl., 65, 1775-1785, (2013) · Zbl 1339.93013
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.