Koofigar, Hamid Reza; Sheikholeslam, Farid; Hosseinnia, Saeed Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua’s circuit. (English) Zbl 1317.34087 Chaos 21, No. 4, 043134, 9 p. (2011). Summary: The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are \(L_{2}\) signals, an adaptive control incorporated with \(H_{\infty}\) control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua’s circuits.{©2011 American Institute of Physics} Cited in 9 Documents MSC: 34C28 Complex behavior and chaotic systems of ordinary differential equations 93B36 \(H^\infty\)-control 34D06 Synchronization of solutions to ordinary differential equations 93C40 Adaptive control/observation systems 93D21 Adaptive or robust stabilization PDFBibTeX XMLCite \textit{H. R. Koofigar} et al., Chaos 21, No. 4, 043134, 9 p. (2011; Zbl 1317.34087) Full Text: DOI References: [1] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821 [2] Krstic M., Nonlinear and Adaptive Control Design (1995) [3] DOI: 10.1016/S0016-0032(99)00010-1 · Zbl 1051.93514 · doi:10.1016/S0016-0032(99)00010-1 [4] DOI: 10.1016/j.physleta.2004.07.024 · Zbl 1209.93119 · doi:10.1016/j.physleta.2004.07.024 [5] DOI: 10.1016/j.chaos.2006.06.104 · Zbl 1141.93361 · doi:10.1016/j.chaos.2006.06.104 [6] DOI: 10.1109/81.933330 · doi:10.1109/81.933330 [7] DOI: 10.1016/j.cnsns.2008.10.009 · doi:10.1016/j.cnsns.2008.10.009 [8] DOI: 10.1016/j.chaos.2007.09.076 · doi:10.1016/j.chaos.2007.09.076 [9] DOI: 10.1016/S0960-0779(04)00414-X · doi:10.1016/S0960-0779(04)00414-X [10] DOI: 10.1063/1.3553183 · Zbl 1345.34074 · doi:10.1063/1.3553183 [11] DOI: 10.1016/j.chaos.2006.04.047 · Zbl 1152.93407 · doi:10.1016/j.chaos.2006.04.047 [12] DOI: 10.1016/j.chaos.2009.03.082 · Zbl 1198.93014 · doi:10.1016/j.chaos.2009.03.082 [13] DOI: 10.1016/j.chaos.2006.04.003 · Zbl 1129.93489 · doi:10.1016/j.chaos.2006.04.003 [14] DOI: 10.1016/j.physleta.2004.11.033 · Zbl 1123.37307 · doi:10.1016/j.physleta.2004.11.033 [15] DOI: 10.1016/j.nonrwa.2007.05.009 · Zbl 1154.34334 · doi:10.1016/j.nonrwa.2007.05.009 [16] DOI: 10.1016/j.chaos.2009.04.044 · Zbl 1198.93112 · doi:10.1016/j.chaos.2009.04.044 [17] DOI: 10.1063/1.3013601 · Zbl 1309.34076 · doi:10.1063/1.3013601 [18] DOI: 10.1016/j.ymssp.2007.08.007 · doi:10.1016/j.ymssp.2007.08.007 [19] DOI: 10.1016/j.chaos.2007.11.019 · Zbl 1198.34123 · doi:10.1016/j.chaos.2007.11.019 [20] DOI: 10.1016/j.chaos.2007.01.092 · Zbl 05807295 · doi:10.1016/j.chaos.2007.01.092 [21] DOI: 10.1016/j.chaos.2005.11.049 · doi:10.1016/j.chaos.2005.11.049 [22] DOI: 10.1016/j.chaos.2005.05.055 · Zbl 1089.94048 · doi:10.1016/j.chaos.2005.05.055 [23] DOI: 10.1016/j.physleta.2005.07.079 · Zbl 1195.94105 · doi:10.1016/j.physleta.2005.07.079 [24] DOI: 10.1049/iet-cta:20060148 · doi:10.1049/iet-cta:20060148 [25] DOI: 10.1109/TAC.2004.825612 · Zbl 1365.93249 · doi:10.1109/TAC.2004.825612 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.