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Stability analysis based on partition trajectory approach for switched neural networks with fractional Brown noise disturbance. (English) Zbl 1380.93278
Summary: In this brief, the stability problem based on feedback control for two types of stochastic neural networks driven by fractional Brown noise is considered. One class is the switched neural networks without time delays and the other one is with time delays. A novel analysis method, very different to the usual approach based on the Itô formula and infinitesimal operator, is proposed in this paper. By the idea of splitting time of trajectory and associating with Hölder inequality, some criteria are obtained to guarantee the switched neural networks with two types to be stable. In the end, two numerical examples and auxiliary figures are presented to show the feasibility and effectiveness for the proposed results.

MSC:
93E15 Stochastic stability in control theory
93D15 Stabilization of systems by feedback
93E03 Stochastic systems in control theory (general)
93D20 Asymptotic stability in control theory
60G22 Fractional processes, including fractional Brownian motion
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[1] Bai, R. (2015). Neural network control-based adaptive design for a class of DC motor systems with the full state constraints. Neurocomputing, 168, 65-69.
[2] Cao, J., Rakkiyappan, R., & Maheswari, K. (2016). Exponential H_∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Science China Technological Sciences, 59(3), 387-402.
[3] Caraballo, T., Garrido-Atienza, M., & Taniguchi, T. (2011). The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion. Nonlinear Analysis: Theory, Methods & Applications, 74(11), 3671-3684. · Zbl 1218.60053
[4] Chen, Y., & Zheng, W. (2013). Stability analysis of time-delay neural networks subject to stochastic perturbations. IEEE Transactions on Cybernetics, 43(6), 2122-2134.
[5] Duncan, T., Maslowski, B., & Pasik-Duncan, B. (2005). Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise. Stochastic Processes and Their Applications, 115, 1357-1383. · Zbl 1076.60054
[6] Gardner, D. (1989). Noise modulation of synaptic weights in a biological neural network. Neural Networks, 2(1), 69-76.
[7] Ge, C., Hua, C., & Guan, X. (2014). New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach. IEEE Transactions on Neural Networks and Learning Systems, 25(7), 1378-1383.
[8] Haykin, S. (1994). Neural networks. Upper Saddle River, NJ: Prentice-Hall. · Zbl 0828.68103
[9] He, Y., Liu, G., & Rees, D. (2007). New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Transactions on Neural Networks and Learning Systems, 18(1), 310-314.
[10] Li, T., Guo, L., Sun, C., & Lin, C. (2008). Further results on delay-dependent stability criteria of neural networks with time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 19(4), 726-730.
[11] Li, T., Wang, T., Song, A., & Fei, S. (2013). Combined convex technique on delay-dependent stability for delayed neural networks. IEEE Transactions on Neural Networks and Learning Systems, 24(9), 1459-1466.
[12] Li, X., Chao, J., & Kang, W. (2015). Trajectory tracking of nonlinear system using multiple series-parallel dynamic neural networks. Neurocomputing, 168(30), 1-12.
[13] Liang, J., Wang, Z., Liu, Y., & Liu, X. (2008). Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks. IEEE Transactions on Neural Networks and Learning Systems, 19(11), 1910-1921.
[14] Mamadou, A., & Maria, F. (2014). Retarded evolution systems driven by fractional Brownian motion with Hurst parameter ##img####img####img##H>12. Nonlinear Analysis: Theory, Methods & Applications, 97, 15-29. · Zbl 1287.34067
[15] Mao, X., & Yuan, C. (2006). Stochastic differential equations with Markovian switching. London: Imperial College Press. · Zbl 1126.60002
[16] Marohasy, J., & Abbot, J. (2015). Assessing the quality of eight different maximum temperature time series as inputs when using artificial neural networks to forecast monthly rainfall at Cape Otway, Australia. Atmosphere Research, 166, 141-149.
[17] Mishura, Y. (2008). Stochastic calculus for fractional Brownian motion and related processes. Berlin Heidelberg: Springer -Verlag. · Zbl 1138.60006
[18] Pabisek, E., & Waszczyszyn, Z. (2015). Identification of thin elastic isotropic plate parameters applying guided wave measurement and artificial neural networks. Mechanical Systems and Signal Processing, 64-65, 403-412.
[19] Sun, Y., & Cao, J. (2007). Pth moment exponential stability of stochastic recurrent neural networks with time-varying delays. Nonlinear Analysis: Real World Applications, 8(4), 1171-1185. · Zbl 1196.60125
[20] Tang, Y., & Wong, W. (2013). Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Transactions on Neural Networks and Learning Systems, 24(3), 435-447.
[21] Wang, Z., Liu, L., Shan, Q., & Zhang, H. (2015). Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE Transactions on Neural Networks and Learning Systems, 26(10), 2589-2595.
[22] Wu, X., Tang, Y., & Zhang, W. (2014). Stability analysis of wwitched stochastic neural networks with time-varying delays. Neural Networks, 51, 39-49. · Zbl 1302.93235
[23] Wu, Z., Lam, J., Su, H., & Chu, J. (2012). Stability and dissipativity analysis of static neural networks with time delay. IEEE Transactions on Neural Networks and Learning Systems, 23(2), 199-210.
[24] Wu, Z., Shi, P., Su, H., & Chu, J. (2013). Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data. IEEE Transactions on Cybernetics, 43(6), 1796-1806.
[25] Wu, Z., Su, H., Chu, J., & Zhou, W. (2009). New results on robust exponential stability for discrete recurrent neural networks with time-varying delays. Neurocomputing, 72(13-15), 3337-3342.
[26] Yang, J., Zhou, W., Shi, P., Yang, X., Zhou, X., & Su, H. (2015). Adaptive synchronization of delayed Markovian switching neural networks with Lévy noise. Neurocomputing, 156(25), 231-238. · Zbl 1348.34097
[27] Yu, L., Fei, S., Sun, L., & Huang, J. (2015). Design of robust adaptive neural switching controller for robotic manipulators with uncertainty and disturbances. The Journal of Intelligent and Robotic Systems, 77(3-4), 571-581.
[28] Yu, L., Fei, S., Sun, L., Huang, J., & Zhu, Y. (2015). Fuzzy approximation of a novel nonlinear adaptive switching controller design. Circuits, Systems, & Signal Processing, 34(2), 377-391. · Zbl 1341.93048
[29] Yu, L., Fei, S., & Yang, G. (2015). A neural network approach for tracking control of uncertain switched nonlinear systems with unknown dead-zone input. Circuits, Systems, and Signal Processing, 34, 2695-2710. · Zbl 1341.93049
[30] Yu, L., Zhang, M., & Fei, S. (2013). Non-linear adaptive sliding mode switching control with average dwell-time. International Journal of Systems Science, 44(3), 471-478. · Zbl 1307.93088
[31] Zhang, W., Tang, Y., Fang, J., & Wu, X. (2012). Stability of delayed neural networks with time-varying impulses. Neural Networks, 36, 59-63. · Zbl 1258.34166
[32] Zhang, W., Tang, Y., Miao, Q., & Du, W. (2013). Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Transactions on Neural Networks and Learning Systems, 24(8), 1316-1326.
[33] Zhang, W., Tang, Y., Wong, W., & Miao, Q. (2015). Stochastic stability of delayed neural networks with local impulsive effects. IEEE Transactions on Neural Networks and Learning Systems, 26(10), 2336-2344.
[34] Zhou, X., Zhou, W., Dai, A., & Yang, J. (2015). Asymptotical stability of stochastic neural networks with multiple time-varying delays. International Journal of Control, 88(3), 613-621. · Zbl 1328.93222
[35] Zhou, X., Zhou, W., Yang, J., & Hu, J. (2015a). A novel scheme for synchronization control of stochastic neural networks with multiple time-varying delays. Neurocomputing, 159, 50-57.
[36] Zhou, X., Zhou, W., Yang, J., & Hu, X. (2015b). Stochastic synchronization of neural networks with multiple time-varying delays and Markovian jump. The Journal of The Franklin Institute, 352(3), 1265-1283. · Zbl 1307.93391
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