Finite-time stabilization of three-dimensional chaotic systems based on CLF. (English) Zbl 1237.34093

Yu, Wenguang

Phys. Lett., A 374, No. 30, 3021-3024 (2010).

Summary: This Letter investigates the stabilization of three-dimensional chaotic systems in a finite time. Based on the finite-time stability theory, a control law is proposed to realize finite-time chaos stabilization of three-dimensional chaotic systems. Several illustrative examples with numerical simulations are studied by using the results obtained in this Letter. Study of examples shows that our control methods work very well in stabilizing a class of chaotic systems in a finite time.

MSC:

34C28	Complex behavior and chaotic systems of ordinary differential equations
34H10	Chaos control for problems involving ordinary differential equations
34K20	Stability theory of functional-differential equations

Keywords:

chaos; chaos control; finite-time stabilization; CLF

References:

[1]	Ott, E.; Grebogi, C.; Yorke, J. A., Phys. Rev. Lett., 64, 1196 (1990)
[2]	Boccaletti, S.; Grebogi, C.; Lai, Y. C., Phys. Rep., 329, 103 (2000)
[3]	Yang, L.; Liu, Z. R.; Mao, J. M., Phys. Rev. Lett., 84, 67 (2000)
[4]	Singer, J.; Wang, Y. Z.; Bau, H. H., Phys. Rev. Lett., 66, 1123 (1991)
[5]	Auerbach, D.; Grebogi, C.; Ott, E.; Yorke, J. A., Phys. Rev. Lett., 69, 3479 (1992)
[6]	Yu, W. G., Phys. Lett. A, 374, 1488 (2010)
[8]	Haimo, V. T., SIAM J. Control Optim., 24, 760 (1986)
[9]	Wang, H.; Han, Z. Z., Nonlinear Anal.: Real World Appl., 10, 2842 (2009)
[10]	Wang, H.; Han, Z. Z., Commun. Nonlinear Sci. Numer. Simul., 14, 2239 (2009)
[11]	Lü, J. H.; Chen, G. R.; Cheng, D. Z., Int. J. Bifur. Chaos, 12, 2917 (2002)
[12]	Dadras, S.; Momeni, H. R., Phys. Lett. A, 373, 3637 (2009) · Zbl 1233.37022
[13]	Genesio, R.; Tesi, A., Automatica, 28, 531 (1992)
[14]	Tigan, G.; Opris, D., Chaos Solitons Fractals, 36, 1315 (2008)