Sliding Mode Control of the Fractional-Order Unified Chaotic System

This paper deals with robust synchronization of the fractional-order unified chaotic systems. Firstly, control design for synchronization of nominal systems is proposed via fractional sliding mode technique. Then, systematic uncertainties and external disturbances are considered in the fractional-order unified chaotic systems, and adaptive sliding mode control is designed for the synchronization issue. Finally, numerical simulations are carried out to verify the effectiveness of the two proposed control techniques.

[1]  D. Baleanu,et al.  Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control , 2012 .

[2]  Bao Shi,et al.  Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems , 2013 .

[3]  Jie Li,et al.  Chaos in the fractional order unified system and its synchronization , 2008, J. Frankl. Inst..

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

[5]  S. Bhalekar,et al.  Synchronization of different fractional order chaotic systems using active control , 2010 .

[6]  YangQuan Chen,et al.  Fractional order control - A tutorial , 2009, 2009 American Control Conference.

[7]  Qigui Yang,et al.  Parameter identification and synchronization of fractional-order chaotic systems , 2012 .

[8]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.

[9]  Suwat Kuntanapreeda,et al.  Robust synchronization of fractional-order unified chaotic systems via linear control , 2012, Comput. Math. Appl..

[10]  Li Xinjie,et al.  Prediction-control based feedback control of a fractional order unified chaotic system , 2011, 2011 Chinese Control and Decision Conference (CCDC).

[11]  Shangbo Zhou,et al.  Chaos in a fractional-order Rössler system , 2009 .

[12]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[13]  Jun-Guo Lu,et al.  Chaotic dynamics and synchronization of fractional-order Arneodo’s systems , 2005 .

[14]  Dumitru Baleanu,et al.  A note on stability of sliding mode dynamics in suppression of fractional-order chaotic systems , 2013, Comput. Math. Appl..

[15]  D. Baleanu,et al.  Discrete fractional logistic map and its chaos , 2014 .

[16]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

[17]  J. A. Tenreiro Machado,et al.  Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order , 2007 .

[18]  Ivo Petras,et al.  A note on the fractional-order Chua’s system , 2008 .

[19]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .

[20]  Elsayed Ahmed,et al.  On chaos control and synchronization of the commensurate fractional order Liu system , 2013, Commun. Nonlinear Sci. Numer. Simul..

[21]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[22]  Shangbo Zhou,et al.  Chaos synchronization of the fractional-order Chen's system , 2009 .

[23]  Kehui Sun,et al.  Chaos synchronization between two different fractional-order hyperchaotic systems , 2011 .

[24]  Junzhi Yu,et al.  Dynamic analysis of a fractional-order Lorenz chaotic system , 2009 .

[25]  K. Diethelm The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[26]  Xing-yuan Wang,et al.  Dynamic analysis of the fractional-order Liu system and its synchronization. , 2007, Chaos.

[27]  Sara Dadras,et al.  Control of a fractional-order economical system via sliding mode , 2010 .

[28]  M. P. Aghababa Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller , 2012 .

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

[30]  Mohammad Saleh Tavazoei,et al.  Comments on “Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control” [Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762] , 2011 .

[31]  Juhn-Horng Chen,et al.  Chaotic dynamics of the fractionally damped van der Pol equation , 2008 .

[32]  Sara Dadras,et al.  Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ , 2013 .

[33]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[34]  Juebang Yu,et al.  Synchronization of fractional-order chaotic systems , 2005, Proceedings. 2005 International Conference on Communications, Circuits and Systems, 2005..

[35]  Wei-Ching Chen,et al.  Nonlinear dynamics and chaos in a fractional-order financial system , 2008 .

[36]  A. E. Matouk,et al.  Chaos, feedback control and synchronization of a fractional-order modified Autonomous Van der Pol–Duffing circuit , 2011 .

[37]  Nathalie Corson,et al.  Synchronization of Chaotic fractional-Order Systems via Linear Control , 2010, Int. J. Bifurc. Chaos.

[38]  Wenqiang Ji,et al.  Adaptive Sliding Mode Control of a Novel Class of Fractional Chaotic Systems , 2013 .

[39]  I. Podlubny Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[40]  Mohammad Saleh Tavazoei,et al.  Robust synchronization of perturbed Chen's fractional-order chaotic systems , 2011 .

[41]  Daolin Xu,et al.  Chaos synchronization of the Chua system with a fractional order , 2006 .

[42]  Daizhan Cheng,et al.  Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

[43]  Junguo Lu Chaotic dynamics of the fractional-order Lü system and its synchronization , 2006 .

[44]  Changpin Li,et al.  The synchronization of three fractional differential systems , 2007 .

[45]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[46]  Reza Ghaderi,et al.  Synchronization of Fractional-Order Chaotic System via Adaptive PID Controller , 2010 .

[47]  Shouming Zhong,et al.  Design of sliding mode controller for a class of fractional-order chaotic systems , 2012 .

[48]  Mohammad Saleh Tavazoei,et al.  Chaotic attractors in incommensurate fractional order systems , 2008 .

[49]  Zaid Odibat,et al.  A note on phase synchronization in coupled chaotic fractional order systems , 2012 .

[50]  Milad Siami,et al.  More Details on Analysis of Fractional-order Van der Pol Oscillator , 2009 .

[51]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[52]  Changpin Li,et al.  A survey on the stability of fractional differential equations , 2011 .

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

[54]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[55]  Changpin Li,et al.  On chaos synchronization of fractional differential equations , 2007 .