Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems. (English) Zbl 1198.93155

Summary: A robust adaptive neural network synchronization controller is proposed for two chaotic systems with input time delay and uncertainty. The studied chaotic system may possess a wide class of nonlinear time-delayed input uncertainty. The radial basis function (RBF) neural network is used to approximate the unknown continuous bounded function item of the time delay uncertainty via appropriate weight value updated law. With the output of RBF neural network, a robust adaptive synchronization control scheme is presented for the time delay uncertain chaotic system. Finally, a simulation example is used to illustrate the effectiveness of the proposed synchronization control scheme.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.


93D09 Robust stability
93C40 Adaptive control/observation systems
Full Text: DOI


[1] Elabbasy, E.M.; Agiza, H.N.; EI-Dessoky, M.M., Adaptive synchronization of a hyperchaotic system with uncertain parameter, Chaos, solitons & fractals, 30, 1133-1142, (2006) · Zbl 1142.37325
[2] Zhang, H.H.; Huang, W.; Wang, Z.L.; Chai, T.Y., Adaptive synchronization between two different chaotic systems with unknown parameters, Phys lett A, 24, 890-893, (2007)
[3] Park, Ju H., Chaos synchronization between two different chaotic dynamical systems, Chaos, solitons & fractals, 27, 549-554, (2006) · Zbl 1102.37304
[4] Yau, H.T., Design of adaptive sliding mode controller for chaos synchronization with uncertainties, Chaos, solitons & fractals, 22, 341-347, (2004) · Zbl 1060.93536
[5] Bowong, S.; Moukam Kakmeni, F.M., Synchronization of uncertain chaotic systems via backstepping approach, Chaos, solitons & fractals, 21, 999-1011, (2004) · Zbl 1045.37011
[6] Chen, M.; Jiang, C.S.; Wu, Q.X.; Chen, W.H., Synchronization scheme for uncertain chaotic systems via RBF neural network, Chin phys lett, 350, 363-366, (2006)
[7] Chen, M.; Jiang, C.S.; Jiang, B.; Wu, Q.X., Sliding mode synchronization controller design with neural network for uncertain chaotic systems, Chaos, solitons & fractals, 39, 1856-1863, (2009) · Zbl 1197.93120
[8] Noriega, J.R.; Wang, H., A direct adaptive neural-network control for unknown nonlinear systems and its application, IEEE trans neural netw, 9, 27-34, (1998)
[9] Ge, S.S.; Wang, C., Adaptive neural control of uncertain MIMO nonlinear systems, IEEE trans neural netw, 15, 674-692, (2004)
[10] Ge, S.S.; Hong, F.; Lee, T.H., Adaptive neural network control of nonlinear systems with unknown time delays, IEEE trans automatic control, 48, 2004-2010, (2003) · Zbl 1364.93392
[11] Nguang, S.K., Robust stabilization of a class of time-delay nonlinear systems, IEEE trans automatic control, 45, 756-762, (2000) · Zbl 0978.93067
[12] Xu, S.Y.; Dooren, P.V.; Stefan, R.; Lam, J., Robust stability and stabilization for singular systems with state delay and parameter uncertainty, IEEE trans automatic control, 47, 1122-1128, (2002) · Zbl 1364.93723
[13] Zhu, S.Q.; Zhang, C.H.; Cheng, Z.L.; June, Feng, Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems, IEEE trans automatic control, 52, 880-885, (2007) · Zbl 1366.93478
[14] Lee, Y.S.; Moonb, Y.S.; Kwon, W.H.; Park, P.G., Delay-dependent robust H control for uncertain systems with a state-delay, Automatica, 40, 65-72, (2004) · Zbl 1046.93015
[15] Chen, M.; Jiang, C.S.; Wu, Q.X.; Chen, W.H., Maintaining synchronization by decentralized feedback control in time delay neural networks with parameter uncertainties, Int J neural syst, 17, 115-122, (2007)
[16] Wen, G.L.; Wang, Q.G.; Lin, C.; Han, X.; Li, G.Y., Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays chaos, Solitons & fractals., 29, 1142-1146, (2006) · Zbl 1142.93430
[17] Bowong, S.; Moukam Kakmeni, F.M.; Dimi, J.L.; Koina, R., Synchronizing chaotic dynamics with uncertainties using a predictable synchronization delay design, Commun nonlinear sci numerical simulation, 11, 973-987, (2006) · Zbl 1130.37358
[18] Lin, J.S.; Liao, T.L.; Yan, J.J.; Yau, H.T., Synchronization of unidirectional coupled chaotic systems with unknown channel time-delay: adaptive robust observer-based approach, Chaos, solitons & fractals, 26, 971-978, (2005) · Zbl 1093.93535
[19] Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A., Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays, Chaos, solitons & fractals., 29, 838-844, (2006) · Zbl 1142.93429
[20] Shahverdiev, E.M.; Nuriev, R.A.; Hashimov, R.H.; Shore, K.A., Chaos synchronization between the MacKey-Glass systems with multiple time delays, Chaos, solitons & fractals., 29, 854-861, (2006) · Zbl 1142.37330
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