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A simple universal adaptive feedback controller for chaos and hyperchaos control. (English) Zbl 1219.93111
Summary: A simple universal adaptive feedback controller is proposed for chaos control. In comparison with previous methods, the proposed scheme, which uses a single feedback gain and converges very fast, is suitable for application to a larger class of chaotic, hyperchaotic and nonhyperbolic chaotic systems. A sufficient condition for selecting the least feedback terms is given, and a numerical example using the Lorenz system verifies the correctness and effectiveness of the proposed approach.
MSC:
93D21Adaptive or robust stabilization
93D15Stabilization of systems by feedback
34H10Chaos control (ODE)
37D45Strange attractors, chaotic dynamics
37N35Dynamical systems in control
References:
[1]Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos, Phys. rev. Lett. 64, 1196-1199 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[2]Boccaletti, S.; Grebogi, C.; Lai, Y. C.: The control of chaos: theory and application, Phys. rep. 329, 103-197 (2000)
[3]Schöll, E.; Schuster, H. G.: Handbook of chaos control, (2008)
[4]Corron, N. J.; Pethel, S. D.; Hopper, B. A.: Controlling chaos with simple limiters, Phys. rev. Lett. 84, 3835-3838 (2000)
[5]Water, W.; Weger, J.: Failure of chaos control, Phys. rev. E 62, 6398-6408 (2000)
[6]Huang, D.: Failure of the ott–grebogi–York-type controllers for nonhyperbolic chaos, Chin. phys. Lett. 19, 762-764 (2002)
[7]Huang, D.: Stabilizing near-nonhyperbolic chaotic systems with applications, Phys. rev. Lett. 93, 214101 (2004)
[8]Arecchi, F. T.; Boccaletti, S.: Adaptive strategies for recognition, noise filtering, control, synchronization and targeting of chaos, Chaos 7, 621-634 (1997) · Zbl 0938.37054 · doi:10.1063/1.166262 · doi:http://ojps.aip.org/journal_cgi/getabs?KEY=CHAOEH&cvips=CHAOEH000007000004000621000001&gifs=Yes
[9]Wang, X. F.: Slower speed and stronger coupling: adaptive mechanisms of chaos synchronization, Phys. rev. E 65, 067202 (2002)
[10]Vincent, U. E.: Synchronization of Rikitake chaotic attractor using active control, Phys. lett. A 343, 133-138 (2005) · Zbl 1194.34091 · doi:10.1016/j.physleta.2005.06.003
[11]Vincent, U. E.: Controlling directed transport in inertia ratchets via adaptive back-stepping control, Acta phys. Polon. B 38, 2459-2469 (2007)
[12]Huang, D.: Simple adaptive-feedback controller for identical chaos synchronization, Phys. rev. E 71, 037203 (2005)
[13]Chen, M.; Zhou, D.: Synchronization in uncertain complex networks, Chaos 16, 013101 (2006) · Zbl 1144.37338 · doi:10.1063/1.2126581
[14]Hu, M.; Xu, Zh.: Adaptive projective synchronization of unified chaotic systems and its application to secure communication, Chin. phys. 16, 3231-3237 (2007)
[15]Huang, D.: Adaptive-feedback control algorithm, Phys. rev. E 73, 066204 (2006)