Chen, Bing; Liu, Xiaoping; Tong, Shaocheng Adaptive fuzzy approach to control unified chaotic systems. (English) Zbl 1142.93356 Chaos Solitons Fractals 34, No. 4, 1180-1187 (2007). Summary: An adaptive fuzzy control method is developed to control unified chaotic systems. Fuzzy logic systems are used to approximate nonlinear functions in the chaotic system and an adaptive technique is employed to construct controllers, which drive state variables into a small neighborhood of the origin. The simulation results are provided to demonstrate the effectiveness and feasibility of the proposed method. Cited in 16 Documents MSC: 93C40 Adaptive control/observation systems 93C42 Fuzzy control/observation systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 93D21 Adaptive or robust stabilization PDFBibTeX XMLCite \textit{B. Chen} et al., Chaos Solitons Fractals 34, No. 4, 1180--1187 (2007; Zbl 1142.93356) Full Text: DOI References: [1] Ott, E.; Grebogi, C.; Yorke, J. K., Controlling chaos, Phys Rev Lett, 64, 1196-9199 (1999) [2] Fuh, C. C.; Tung, P. C., Controlling chaos using differential geometric method, Phys Rev Lett, 75, 2952-2955 (1995) [3] Wang, Y.; Guan, Z.; Wen, X., Adaptive synchronization for Chen chaotic system with fully unknown parameters, Chaos, Solitons & Fractals, 19, 899-903 (2004) · Zbl 1053.37528 [4] Wu, X.; Lu, J., Adaptive control of uncertain Lü system, Chaos, Solitons & Fractals, 22, 375-381 (2004) · Zbl 1062.93516 [5] Feki, M., An adaptive feedback control of linearizable chaotic systems, Chaos, Solitons & Fractals, 15, 883-890 (2003) · Zbl 1042.93510 [6] Wang, L. X.; Mendel, J. M., Fuzzy basis functions, universal approximation, and orthogonal least squares learning, IEEE Trans Neural Networks, 3, 5, 807-814 (1992) [7] Wang, L. X., Adaptive fuzzy systems and control: design and stability (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ [8] Lü, J.; Chen, G.; Chen, D.; Čelikoveskyˇ, S., Bridge the gap between the Lorenz system and the Chen system, Int J Bifurc Chaos, 12, 2917-2926 (2002) · Zbl 1043.37026 [9] Lu, J.; Wu, X.; Lu, J., Synchronization of a unified chaotic system and application in secure communication, Phys Lett A, 305, 365-370 (2002) · Zbl 1005.37012 [10] Chen, S.; Lü, J., Synchronization of an uncertain unified chaotic system via adaptive control, Chaos, Solitons & Fractals, 14, 643-647 (2002) · Zbl 1005.93020 [11] Wu, X.; Lu, J., Parameter identification and backstepping control of uncertain Lü system, Chaos, Solitons & Fractals, 18, 721-729 (2003) · Zbl 1068.93019 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.