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Controlling the Fractional-Order Chaotic System Based on Inverse Optimal Control Approach

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Abstract:

In this paper, we numerically investigate the chaotic behaviors of a fractional-order system. We find that chaotic behaviors exist in the fractional-order system with an order being less than 3. The lowest order we find to have chaos is 2.4 in such system. In addition, we numerically simulate the continuances of the chaotic behaviors in the fractional-order system with orders ranging from 2.7 to 3. Finally, a simple, but effective, linear state feedback controller is proposed for controlling the fractional-order chaotic system based on an inverse optimal control approach. Numerical simulations show the effectiveness and feasibility of the proposed controller.

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Periodical:

Key Engineering Materials (Volumes 474-476)

Pages:

108-113

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.474-476.108

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Online since:

April 2011

Authors:

Xin Gao

Keywords:

Chaos, Control, Fractional Derivative, Fractional Integral

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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References

[1] R.C. Koeller：J. Appl. Mech., Vol. 51(1984), p.299.

Google Scholar

[2] M. Ichise, Y. Nagayanagi and T. Kojima：J. Electroanal. Chem., Vol. 33(1971), p.253.

Google Scholar

[3] T.T. Hartly, C.F. Lorenzo and H.K. Qammer：IEEE Trans. CAS-I: Fundamental Theory and Applications, Vol. 42(1995), p.485.

Google Scholar

[4] W.M. Ahmad and J.C. Sprott：Chaos, Solitons & Fractals. Vol. 16(2003), p.339.

Google Scholar

[5] W.M. Ahmad and A.M. Harb：Chaos, Solitons & Fractals. Vol. 18(2003), p.693.

Google Scholar

[6] C. Li, X. Liao and J. Yu: Phys Rev E. Vol. 68 (2003), 067203.

Google Scholar

[7] C.G. Li and G.R. Chen: Physica A. Vol. 341(2004), pp.55-61.

Google Scholar

[8] X. Gao and J.B. Yu: Chaos, Solitons & Fractals. Vol. 24(2005), p.1097.

Google Scholar

[9] I. Podlubny：Fractional differential equations. New York: Academic Press, (1999).

Google Scholar

[10] A. Charef, H.H. Sun, Y.Y. Tsao and B. Onaral: IEEE Trans. Autom Control. Vol. 37(1992), p.1465.

Google Scholar

[11] C.X. Liu, T. Liu, L. Liu and K. Liu: Chaos, Solitons & Fractals. Vol. 22 (2004), p.1031.

Google Scholar

[12] E. Ott, C. Grebogi and J.A. Yorke: Phys Rev Lett., Vol. 64 (1990), p.1196.

Google Scholar

[13] G.R. Chen: Dynamics of a class the Lorenz systems: analysis, control and synchronization. Beijing: Science press, (2003).

Google Scholar

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