Stabilization of fractional chen chaotic system by linear feedback control

This paper investigates the linear feedback control of the fractional-order Chen chaotic system. The analysis and implementation of the control system in the frequency domain is realized by mean of Charef's singularity function method. A numerical simulation shows the effectiveness of the proposed controller in stabilizing the system on an unstable fixed point and a periodic orbit.

[1]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[2]  Guanrong Chen,et al.  A note on the fractional-order Chen system , 2006 .

[3]  Mohammad Saleh Tavazoei,et al.  Chaos control via a simple fractional-order controller , 2008 .

[4]  Li Tian-Zeng,et al.  Control of fractional chaotic and hyperchaotic systems based on a fractional order controller , 2014 .

[5]  Samir Ladaci,et al.  Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller , 2017 .

[6]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[7]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[8]  Qidan Zhu,et al.  Adaptive chatter free sliding mode control for a class of uncertain chaotic systems , 2014, Appl. Math. Comput..

[9]  Giuseppe Grassi,et al.  Bifurcation and chaos in the fractional Chua and Chen systems with very low order , 2009, 2009 IEEE International Symposium on Circuits and Systems.

[10]  Hsien-Keng Chen,et al.  Chaos in a new system with fractional order , 2007 .

[11]  H. Momeni,et al.  Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems , 2013 .

[12]  B. Onaral,et al.  Fractal system as represented by singularity function , 1992 .

[13]  Chunguang Li,et al.  Chaos in the fractional order Chen system and its control , 2004 .

[14]  Changpin Li,et al.  Chaos in Chen's system with a fractional order , 2004 .

[15]  Bao Shi,et al.  Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems , 2015 .

[16]  Samir Ladaci,et al.  On Fractional Adaptive Control , 2006 .

[17]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[18]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.