A hyperchaotic system stabilization via inverse optimal control and experimental research

doi:10.1088/1674-1056/19/10/100502

Abstract In this paper, some basic dynamical properties of a four-dimensional autonomous hyperchaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this new hyperchaotic system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment. An efficient approaching is developed for global asymptotic stabilization of this four-dimensional hyperchaotic system. Based on the method of inverse optimal control for nonlinear systems, a linear state feedback is electronically implemented. It is remarkably simple as compared with other chaos control ways, like nonlinear state feedback.

Keywords: hyperchaos inverse optimal control numerical simulation circuitry experiment

Received: 29 March 2010
Revised: 27 April 2010
Accepted manuscript online:

PACS:	02.30.Oz	(Bifurcation theory)
	02.30.Uu	(Integral transforms)
	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

Cite this article:

Yang Ning-Ning(杨宁宁), Liu Chong-Xin(刘崇新), and Wu Chao-Jun(吴朝俊) A hyperchaotic system stabilization via inverse optimal control and experimental research 2010 Chin. Phys. B 19 100502

[1]	Rossler O E 1979 Phys. Lett. A 71 155
[2]	Kapitaniak T and Chua L O 1994 Int. J. Bifurc. Chaos 4 477
[3]	Liu C X, Liu T and Liu L 2004 Chaos, Solitons and Fractals 22 1031
[4]	Liu C X 2007 Chin. Phys. 16 3279
[5]	Liu C X and Liu L 2009 Chin. Phys. B 18 2188
[6]	Zhou P, Cao Y X and Cheng X F 2009 Chin. Phys. B 18 1394
[7]	Chen Z Q, Yang Y, Qi G Y and Yuan Z Z 2007 Phys. Lett. A 360 696
[8]	Chen G R and Ueta T 1999 Int. J. Bifurc. Chaos 9 1465
[9]	Sun M, Tian L X and Fu Y 2007 Chaos, Solitons and Fractals 32 168
[10]	Lü J H, Chen G R and Zhang S C 2002 Chaos, Solitons and Fractals 14 669
[11]	Wang F Q and Liu C X 2006 Phys. Lett. A 360 274
[12]	Freeman R A and Kokotovic P V 1996 Siam Journal on Control and Optimization 34 1365
[13]	Sanchez E N, Perez J P, Martinez M and Chen G R 2002 Latin American Applied Research 32 111
[14]	Jimenez A, Sanchez E N, Chen G R and Perez J P 2009 Int. J. Circ. Theor. Appl. 37 887
[15]	Liu C X 2006 Far East Journal of Dynamical Systems 8 231 endfootnotesize

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A hyperchaotic system stabilization via inverse optimal control and experimental research

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