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Adaptive neural network synchronization for uncertain strick-feedback chaotic systems subject to dead-zone input. (English) Zbl 1446.93037

Summary: In this paper, an adaptive neural network (NN) synchronization controller is designed for two identical strict-feedback chaotic systems (SFCSs) subject to dead-zone input. The dead-zone models together with the system uncertainties are approximated by NNs. The dynamic surface control (DSC) approach is applied in the synchronization controller design, and the traditional problem of “explosion of complexity” that usually occurs in the backstepping design can be avoided. The proposed synchronization method guarantees the synchronization errors tend to an arbitrarily small region. Finally, this paper presents two simulation examples to confirm the effectiveness and the robustness of the proposed control method.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
93C40 Adaptive control/observation systems
34H10 Chaos control for problems involving ordinary differential equations
93C42 Fuzzy control/observation systems
93C10 Nonlinear systems in control theory

References:

[1] Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821-824 (1990) · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821
[2] Cao, J., Li, R.: Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci. China Inf. Sci. 60(3), 032201 (2017) · doi:10.1007/s11432-016-0555-2
[3] Wang, H., Liu, P.X., Liu, S.: Adaptive neural synchronization control for bilateral teleoperation systems with time delay and backlash-like hysteresis. IEEE Trans. Cybern. 47(10), 3018-3026 (2017) · doi:10.1109/TCYB.2016.2644656
[4] Lu, J., Ho, D.W.C., Cao, J.: A unified synchronization criterion for impulsive dynamical networks. Automatica 46(7), 1215-1221 (2010) · Zbl 1194.93090 · doi:10.1016/j.automatica.2010.04.005
[5] Liu, H., Pan, Y., Li, S., Chen, Y.: Adaptive fuzzy backstepping control of fractional-order nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. 47, 2209-2217 (2017) · doi:10.1109/TSMC.2016.2640950
[6] Bao, H.B., Cao, J.D.: Projective synchronization of fractional-order memristor-based neural networks. Neural Netw. 63, 1-9 (2015) · Zbl 1323.93036 · doi:10.1016/j.neunet.2014.10.007
[7] Li, G., Liu, H.: Stability analysis and synchronization for a class of fractional-order neural networks. Entropy 18(2), 55 (2016) · doi:10.3390/e18020055
[8] Das, S., Halder, U., Maity, D.: Chaotic dynamics in social foraging swarms-an analysis. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 42(4), 1288-1293 (2012) · doi:10.1109/TSMCB.2012.2186799
[9] Sundarapandian, V., Sivaperumal, S.: Sliding controller design of hybrid synchronization of four-wing chaotic systems. Int. J. Soft Comput. 6(5-6), 224-231 (2011) · doi:10.3923/ijscomp.2011.224.231
[10] Liu, H., Li, S., Cao, J., Li, G., Alsaedi, A., Alsaadi, F.E.: Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances. Neurocomputing 219, 422-430 (2017) · doi:10.1016/j.neucom.2016.09.050
[11] Tu, Z., Cao, J., Alsaedi, A., Alsaadi, F.E., Hayat, T.: Global Lagrange stability of complex-valued neural networks of neutral type with time-varying delays. Complexity 21(S2), 438-450 (2016) · doi:10.1002/cplx.21823
[12] Liu, H., Li, S., Li, G., Wang, H.: Robust adaptive control for fractional-order financial chaotic systems with system uncertainties and external disturbances. Inf. Technol. Control 46, 246-259 (2017)
[13] Liu, S., Zhou, L.: Network synchronization and application of chaotic Lur’e systems based on event-triggered mechanism. Nonlinear Dyn. 83(4), 2497-2507 (2016) · Zbl 1353.94092 · doi:10.1007/s11071-015-2498-y
[14] Liu, H., Chen, Y., Li, G., Xiang, W., Xu, G.: Adaptive fuzzy synchronization of fractional-order chaotic (hyperchaotic) systems with input saturation and unknown parameters. Complexity 2017, Article ID 6853826 (2017) · Zbl 1377.93094
[15] Cao, J., Sivasamy, R., Rakkiyappan, R.: Sampled-data \(H∞\text{H}_{\infty}\) synchronization of chaotic Lur’e systems with time delay. Circuits Syst. Signal Process. 35(3), 811-835 (2016) · Zbl 1346.93145 · doi:10.1007/s00034-015-0105-6
[16] Chen, X., Cao, J., Ju, H.P., Huang, T., Qiu, J.: Finite-time multi-switching synchronization behavior for multiple chaotic systems with network transmission mode. J. Franklin Inst. 355(5), 2892-2911 (2018) · Zbl 1393.93057 · doi:10.1016/j.jfranklin.2018.01.027
[17] Boulkroune, A., Bouzeriba, A., Hamel, S., Bouden, T.: A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems. Nonlinear Dyn. 78(1), 433-447 (2014) · Zbl 1314.93030 · doi:10.1007/s11071-014-1450-x
[18] Zhao, M., Liu, R., Gao, Y.: Dissipative lag synchronization of chaotic Lur’e systems with unknown disturbances. IMA J. Math. Control Inf. 34(1), 123-138 (2017) · Zbl 1397.93047 · doi:10.1093/imamci/dnv034
[19] Liu, B., Liu, X., Chen, G., Wang, H.: Robust impulsive synchronization of uncertain dynamical networks. IEEE Trans. Circuits Syst. I, Regul. Pap. 52(7), 1431-1441 (2005) · Zbl 1374.82016 · doi:10.1109/TCSI.2005.851708
[20] Yu, W., Cao, J.: Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification. Physica A 375(2), 467-482 (2007) · doi:10.1016/j.physa.2006.09.020
[21] Huang, C., Cao, J.: Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system. Physica A 473(2), 526-537 (2017)
[22] Chen, X., Qiu, J., Cao, J., He, H.: Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection. Neurocomputing 173, 1299-1309 (2016) · doi:10.1016/j.neucom.2015.09.003
[23] Liu, H., Pan, Y., Li, S., Chen, Y.: Synchronization for fractional-order neural networks with fullunder-actuation using fractional-order sliding mode control. Int. J. Mach. Learn. Cybern. (2017). https://doi.org/10.1007/s13042-017-0646-z · doi:10.1007/s13042-017-0646-z
[24] Chen, X., Ju, H.P., Cao, J., Qiu, J.: Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances. Appl. Math. Comput. 308, 161-173 (2017) · Zbl 1411.34087
[25] Yu, W., Chen, G., Lü, J., Kurths, J.: Synchronization via pinning control on general complex networks. SIAM J. Control Optim. 51(2), 1395-1416 (2013) · Zbl 1266.93071 · doi:10.1137/100781699
[26] Yang, X., Cao, J., Lu, J.: Stochastic synchronization of coupled neural networks with intermittent control. Phys. Lett. A 373(36), 3259-3272 (2009) · Zbl 1233.34020 · doi:10.1016/j.physleta.2009.07.013
[27] Cheng, L., Chen, X., Qiu, J., Lu, J., Cao, J.: Aperiodically intermittent control for synchronization of switched complex networks with unstable modes via matrix ω-measure approach. Nonlinear Dyn. 2, 1-12 (2018)
[28] Pan, Y., Liu, Y., Xu, B., Yu, H.: Hybrid feedback feedforward: an efficient design of adaptive neural network control. Neural Netw. 76, 122-134 (2015) · Zbl 1415.93147 · doi:10.1016/j.neunet.2015.12.009
[29] Wu, J., Chen, W., Li, J.: Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy. Fuzzy Sets Syst. 273(8), 1-25 (2015) · Zbl 1373.93197 · doi:10.1016/j.fss.2014.10.009
[30] Tu, Z., Cao, J., Hayat, T.: Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks. Neural Netw. 75, 47-55 (2016) · Zbl 1415.92025 · doi:10.1016/j.neunet.2015.12.001
[31] Pan, Y., Yu, H.: Biomimetic hybrid feedback feedforward neural-network learning control. IEEE Trans. Neural Netw. Learn. Syst. 28(6), 1481-1487 (2017) · doi:10.1109/TNNLS.2016.2527501
[32] Chen, W., Ge, S.S., Wu, J., Gong, M.: Globally stable adaptive backstepping neural network control for uncertain strict-feedback systems with tracking accuracy known a priori. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 1842-1854 (2015) · doi:10.1109/TNNLS.2014.2357451
[33] Boulkroune, A., M’saad, M., Farza, M.: Adaptive fuzzy system-based variable-structure controller for multivariable nonaffine nonlinear uncertain systems subject to actuator nonlinearities. Neural Comput. Appl. 28(11), 3371-3384 (2017) · doi:10.1007/s00521-016-2241-8
[34] Li, G., Cao, J., Alsaedi, A., Ahmad, B.: Limit cycle oscillation in aeroelastic systems and its adaptive fractional-order fuzzy control. Int. J. Mach. Learn. Cybern. 2, 1-9 (2017)
[35] Liu, H., Li, S., Wang, H., Sun, Y.: Adaptive fuzzy control for a class of unknown fractional-order neural networks subject to input nonlinearities and dead-zones. Inf. Sci. 454-455, 30-45 (2018) · Zbl 1448.93181 · doi:10.1016/j.ins.2018.04.069
[36] Liu, H., Li, S., Li, G., Wang, H.: Adaptive controller design for a class of uncertain fractional-order nonlinear systems: an adaptive fuzzy approach. Int. J. Fuzzy Syst. 20(2), 366-379 (2018) · doi:10.1007/s40815-017-0371-5
[37] Lin, D., Wang, X., Nian, F., Zhang, Y.: Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems. Neurocomputing 73(16-18), 2873-2881 (2010) · doi:10.1016/j.neucom.2010.08.008
[38] Pan, Y., Sun, T., Liu, Y., Yu, H.: Composite learning from adaptive backstepping neural network control. Neural Netw. 95, 134-142 (2017) · Zbl 1441.93147 · doi:10.1016/j.neunet.2017.08.005
[39] Ponce, I.U., Bentsman, J., Orlov, Y., Aguilar, L.T.: Generic nonsmooth \(H∞\mathcal{H}_{\infty}\) output synthesis: application to a coal-fired boiler/turbine unit with actuator dead zone. IEEE Trans. Control Syst. Technol. 23(6), 2117-2128 (2015) · doi:10.1109/TCST.2015.2399672
[40] Zhang, T.P., Ge, S.S.: Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44(7), 1895-1903 (2008) · Zbl 1149.93322 · doi:10.1016/j.automatica.2007.11.025
[41] Chen, X., Ju, H.P., Cao, J., Qiu, J.: Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control. Neurocomputing 273, 9-21 (2018) · doi:10.1016/j.neucom.2017.07.063
[42] Tong, S., Li, Y.: Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 20(1), 168-180 (2012) · doi:10.1109/TFUZZ.2011.2171189
[43] Yang, Z., Zhang, H.: A fuzzy adaptive tracking control for a class of uncertain strick-feedback nonlinear systems with dead-zone input. Neurocomputing 272, 130-135 (2017) · doi:10.1016/j.neucom.2017.06.060
[44] Wang, X.-S., Su, C.-Y., Hong, H.: Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica 40(3), 407-413 (2004) · Zbl 1036.93036 · doi:10.1016/j.automatica.2003.10.021
[45] Liu, Y.-J., Gao, Y., Tong, S., Li, Y.: Fuzzy approximation-based adaptive backstepping optimal control for a class of nonlinear discrete-time systems with dead-zone. IEEE Trans. Fuzzy Syst. 24(1), 16-28 (2016) · doi:10.1109/TFUZZ.2015.2418000
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