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An adaptive feedback control of linearizable chaotic systems. (English) Zbl 1042.93510
Summary: This paper proposes an adaptive feedback controller for a class of chaotic systems. This controller can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on Lyapunov approach, the adaptation law is determined to tune the controller gain vector in order to track a predetermined linearizing feedback control. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems namely Chua’s circuit and a Lur’e-like system are considered as illustrative examples.

MSC:
93C10Nonlinear control systems
37D45Strange attractors, chaotic dynamics
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References:
[1] Schiff, S.; Jerger, K.; Duong, D.; Chang, T.; Spano, M.; Ditto, W.: Controlling chaos in the brain. Nature 370, 615-620 (1994)
[2] Garfinkel, A.; Spano, M. L.; Ditto, W. L.; Weiss, J. N.: Controlling cardiac chaos. Science 257, 1230-1235 (1992)
[3] Wu, C. W.; Chua, L. O.: A simple way to synchronize chaotic systems with applications to secure communication systems. Int. J. Bifurcation chaos 3, No. 6, 1619-1627 (1993) · Zbl 0884.94004
[4] Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos. Phys. rev. Lett. 64, 1196-1199 (1990) · Zbl 0964.37501
[5] Boccaletti, S.; Grebogi, C.; Lai, Y. -C.; Maricini, H.; Maza, D.: The control of chaos: theory and applications. Phys. rep. 329, 103-197 (2000)
[6] Yang, S. -K.; C-L, C.; Yau, H. -T.: Control of chaos in Lorenz system. Chaos soliton. Fract. 13, 767-780 (2002) · Zbl 1031.34042
[7] Hwang, C. -C.; Hsieh, J. -Y.; Lin, R. -S.: A linear continuous feedback control of Chua’s circuit. Chaos soliton. Fract. 8, 1507-1515 (1997)
[8] Bernardo, M. D.: An adaptive approach to the control and synchronization of continuous-time chaotic systems. Int. J. Bifurcation chaos 6, No. 3, 557-568 (1996) · Zbl 0900.70413
[9] Tian, Y. -C.; Tade, M. O.; Levy, D.: Constrained control of chaos. Phys. lett. A 296, 87-90 (2002) · Zbl 0994.37025
[10] Hwang, C. -C.; Fung, R. -F.; Hsieh, J. -Y.; Li, W. -J.: A nonlinear feedback control of the Lorenz equation. Int. J. Eng. sci. 37, 1893-1900 (1999) · Zbl 1210.93033
[11] Solak, E.; Morgül, Ö; Ersoy, U.: Observer-based control of a class of chaotic systems. Phys. lett. A 279, No. 1, 47-55 (2001) · Zbl 0972.37020
[12] John, J. K.; Amritkar, A. E.: Synchronization by feedback and adaptive control. Int. J. Bifurcation chaos 4, No. 6, 1687-1695 (1994) · Zbl 0875.93219
[13] Chen, S.; Lü, J.: Synchronization of an uncertain unified chaotic system via adaptive control. Chaos soliton. Fract. 14, 643-647 (2002) · Zbl 1005.93020
[14] Wang, C.; Ge, S.: Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos soliton. Fract. 12, 1199-1206 (2001) · Zbl 1015.37052
[15] Isidori, A.: Nonlinear control systems. (1995) · Zbl 0878.93001
[16] Khalil, H. K.: Nonlinear systems. (1992) · Zbl 0969.34001
[17] Pecora, L. M.; Carroll, T. L.: Driving systems with chaotic signals. Phys. rev. A 44, No. 4, 2374-2383 (1991)