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Impulsive control of Lorenz system. (English) Zbl 0925.93414

Summary: In this paper an impulsive control scheme of the Lorenz system is presented. First we use the theory of impulsive differential equation to find conditions under which impulsively controlled Lorenz system is asymptotically stable. Then we give the estimate of the upper bound of impulse interval for asymptotically stable control. Numerical experimental results are presented.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
34A37 Ordinary differential equations with impulses
34H05 Control problems involving ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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References:

[1] Ott, E.; Grebogi, C.; Yorke, J. A., Phys. Rev. Lett., 64, 1196-1199 (1990) · Zbl 0964.37501
[2] Chen, G.; Dong, X., From chaos to order — Perspectives and methodologies in controlling nonlinear dynamical systems, Int. J. Bifur. Chaos, 3, 1363-1409 (1993) · Zbl 0886.58076
[3] Chua, L. O.; Yang, T.; Zhong, G. Q.; Wu, C. W., Adaptive synchronization of Chua’s Oscillators, Int. J. Bifur. Chaos, 6, 1, 189-201 (1996)
[4] Wu, C. W.; Yang, T.; Chua, L. O., On adaptive synchronization and control of nonlinear dynamical systems, Int. J. Bifur. Chaos, 6, 3, 455-471 (1996) · Zbl 0875.93182
[5] Stojanovski, T.; Kocarev, L.; Parlitz, U., Driving and synchronizing by chaotic impulses, Phys. Rev. E, 54, 2, 2128-2131 (1996)
[6] Yang, T.; Yang, Lin-Bao; Yang, Chun-Mei, Impulsive synchronization of Lorenz systems, Phys. Lett. A, 226, 6, 349-354 (1997)
[7] Yang, T.; Chua, L. O., Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication, Int. J. Bifur. Chaos, 7, 3 (1997), in press · Zbl 0925.93374
[8] Yang, T.; Chua, L. O., Impulsive control and synchronization of chaotic systems and secure communication (29 January 1997), Electronics Research Laboratory, College of Engineering, University of California: Electronics Research Laboratory, College of Engineering, University of California Berkeley, CA 94720, Memorandum No. UCB/ERL M97/12
[9] Lorenz, E. N., J. Atmos. Sci., 20, 130-141 (1990) · Zbl 1417.37129
[10] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
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