Delay-range-dependent local adaptive and robust adaptive synchronization approaches for time-delay chaotic systems
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This paper studies the local adaptive and robust adaptive control methodologies for the synchronization of the chaotic drive and the response systems with finite time lags, bounded delay rates, unknown parameters, and perturbations. A local adaptive coherence control condition under bounded initial condition is developed to synthesize a feedback controller capable of executing successful synchronization of the drive and the response systems with uncertain parameters and delay belonging to a range (with either zero or nonzero lower bound). A sufficiency condition for the adaptive control approach is inculcated through an amendment in the conventional Lyapunov–Krasovskii functional, which enables to develop the adaptation laws for the unknown parameters associated with the nonlinearity in the dynamical behavior of the drive and the response systems. Further, a robust adaptive synchronization control condition for asymptotic convergent behavior of the synchronization error to a bounded region under perturbations as well as disturbances is provided. Indifferent to the existing works, delay-range-dependent adaptive synchronization methodologies are derived in this paper, and the rendered controller design conditions are valid for both the slow and the fast variations in time delays. Numerical simulations for the chaotic delayed Hopfield neural networks are presented to elaborate the efficacy of the proposed delay-range-dependent adaptive and robust adaptive synchronization control methodologies.
KeywordsAdaptive synchronization Robust adaptive synchronization Time-varying delays Lyapunov–Krasovskii functional Local control approach
This work was supported by Higher Education Commission (HEC) of Pakistan by supporting PhD studies of the first author through indigenous PhD scholarship program (phase II, batch II, 2013).
- 8.Wenxiu, Z., Jun, L., Lili, P., Jian, C.: Application of RS485 for communication and synchronization in distributed electromagnetic exploration system. In: Proceedings of Electric Information and Control Engineering (ICEICE), Wuhan, pp. 4815–4818 (2011)Google Scholar
- 13.Tian, J.K., Liu, Y.M.: Improved delay-dependent stability analysis for neural networks with interval time-varying delays. Math. Probl. Eng. Article ID 705367 (2015)Google Scholar
- 14.Rong, R.Z., Tian, J.K.: Improved stability analysis for neural networks with interval time-varying delays. Appl. Mech. Mater. 687, 2078–2082 (2014)Google Scholar
- 15.Guan, Z.H., Liu, Z.W., Feng, G., Wang, Y.W.: Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans. Circuits Syst. I Regul. Pap. 57(8), 2182–2195 (2010)Google Scholar
- 24.Lu, J., Cao, J., Ho, D.W.: Adaptive stabilization and synchronization for chaotic Lur’e systems with time-varying delay. IEEE Trans. Circuits Syst. I Regul. Pap. 55(5), 1347–1356 (2008)Google Scholar
- 30.Ahmad, S., Majeed, R., Hong, K.S., Rehan. M.: Observer design for one-sided Lipschitz nonlinear systems subject to measurement delays. Math. Probl. Eng. Article ID 879492 (2015)Google Scholar
- 35.Ma, J., Qin, H.X., Song, X.L., Chu, R.T.: Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int. J. Mod. Phys. B. 29(01). Article ID 1450239 (2015)Google Scholar