Melnikov's analysis of time-delayed feedback control in chaotic dynamics

作者: Chaohong Cai , Zhenyuan Xu , Wenbo Xu

DOI: 10.1109/TCSI.2002.805738

关键词: Control of chaosHamiltonian systemFeedback controlControl theoryAttractorMathematicsDynamics (mechanics)Orbit (dynamics)ChaoticSynchronization of chaos

摘要: The problem of suppressing chaos in the time-delayed feedback control (TDFC) system is considered. validity Melnikov's technique planar Hamiltonian perturbed by weak periodic terms and time-delay discussed. used to analyze a TDFC chaotic that nonautonomous. It revealed with analytical results delayed time can be independent period inherent unstable orbit attractor. Numerical simulations demonstrate effectiveness analysis.

参考文章(10)
Wolfram Just, Thomas Bernard, Matthias Ostheimer, Ekkehard Reibold, Hartmut Benner, Mechanism of Time-Delayed Feedback Control Physical Review Letters. ,vol. 78, pp. 203- 206 ,(1997) , 10.1103/PHYSREVLETT.78.203
V Basios, T Bountis, G Nicolis, Controlling the onset of homoclinic chaos due to parametric noise Physics Letters A. ,vol. 251, pp. 250- 258 ,(1999) , 10.1016/S0375-9601(98)00892-5
Hiroyuki Nakajima, On analytical properties of delayed feedback control of chaos Physics Letters A. ,vol. 232, pp. 207- 210 ,(1997) , 10.1016/S0375-9601(97)00362-9
Chaohong Cai, Zhenyuan Xu, Wenbo Xu, Bin Feng, Brief Notch filter feedback control in a class of chaotic systems Automatica. ,vol. 38, pp. 695- 701 ,(2002) , 10.1016/S0005-1098(01)00239-4
M. Ashhab, M.V. Salapaka, M. Dahleh, I. Mezić, Brief Paper: Dynamical analysis and control of microcantilevers Automatica. ,vol. 35, pp. 1663- 1670 ,(1999) , 10.1016/S0005-1098(99)00077-1
M. Belhaq, M. Houssni, Suppression of chaos in averaged oscillator driven by external and parametric excitations Chaos Solitons & Fractals. ,vol. 11, pp. 1237- 1246 ,(2000) , 10.1016/S0960-0779(98)00334-8
John Guckenheimer, Philip Holmes, M. Slemrod, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ,(1983)
K. Konishi, M. Ishii, H. Kokame, Stability of extended delayed-feedback control for discrete-time chaotic systems IEEE Transactions on Circuits and Systems I-regular Papers. ,vol. 46, pp. 1285- 1288 ,(1999) , 10.1109/81.795842
Guanrong Chen, Xinghuo Yu, On time-delayed feedback control of chaotic systems IEEE Transactions on Circuits and Systems I-regular Papers. ,vol. 46, pp. 767- 772 ,(1999) , 10.1109/81.768837