Projective synchronization of fractional-order chaotic energy resource systems via linear control based on Takagi-Sugeno fuzzy model

In this paper, the problem of projective synchronization scheme of fractional-order energy resource system based on Takagi-Sugeno fuzzy model is investigated. The scheme is applied to achieve projective synchronization of both three and four dimensional fractional order energy resource systems via linear control approach. A fuzzy linear control and projective schemes are proposed to synchronizes the energy resource system. Numerical simulations of fractional-order energy resource systems are performed by using the Caputo version and a predictor-corrector algorithm for fractional-order differential equations, which is a generalization of the Adams-Bashforth-Moulton method. Finally some numerical simulations show the effectiveness of the proposed results.

[1]  Hsien-Keng Chen,et al.  Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems , 2010 .

[2]  Ruoxun Zhang,et al.  Robust chaos synchronization of fractional-order chaotic systems with unknown parameters and uncertain perturbations , 2012 .

[3]  R. Bagley,et al.  Fractional order state equations for the control of viscoelasticallydamped structures , 1991 .

[4]  Xuerong Shi,et al.  Synchronization of a four-dimensional energy resource system via linear control , 2011 .

[5]  P. Arena,et al.  Chaotic behavior in noninteger-order cellular neural networks , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Ping Ju,et al.  Stochastic synchronization of nonlinear energy resource system via partial feedback control , 2012 .

[7]  Ahmed M. A. El-Sayed,et al.  On the fractional-order logistic equation , 2007, Appl. Math. Lett..

[8]  X. Liao,et al.  Fuzzy modeling and synchronization of hyperchaotic systems , 2005 .

[9]  Lixin Tian,et al.  A new four-dimensional energy resources system and its linear feedback control , 2009 .

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

[11]  Zuolei Wang.  Chaos synchronization of an energy resource system based on linear control , 2010 .

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

[13]  Yibei Nian,et al.  Controlling fractional order chaotic systems based on Takagi-Sugeno fuzzy model and adaptive adjustment mechanism , 2010 .

[14]  Lixin Tian,et al.  Hopf Bifurcation Analysis of the Energy Resource Chaotic System , 2006 .

[15]  E. Ahmed,et al.  On fractional order differential equations model for nonlocal epidemics , 2007, Physica A: Statistical Mechanics and its Applications.

[16]  Lixin Tian,et al.  An energy resources demand–supply system and its dynamical analysis , 2007 .

[17]  Lu Jun-Guo,et al.  Chaotic dynamics and synchronization of fractional-order Genesio–Tesi systems , 2005 .

[18]  Jianying Yang,et al.  Dynamical models of happiness with fractional order , 2010 .

[19]  Xuerong Shi,et al.  Robust chaos synchronization of four-dimensional energy resource system via adaptive feedback control , 2010 .

[20]  A. El-Sayed,et al.  Fractional-order diffusion-wave equation , 1996 .

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

[22]  Alan D. Freed,et al.  Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.

[23]  A. E. M. El Misiery,et al.  On a fractional model for earthquakes , 2006, Appl. Math. Comput..

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

[25]  Xing-yuan Wang,et al.  Projective synchronization of fractional order chaotic system based on linear separation , 2008 .

[26]  Ping Ju,et al.  Robust Stabilization and Synchronization of Nonlinear Energy Resource System via Fuzzy Control Approach , 2012 .

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

[28]  Lixin Tian,et al.  Adaptive control and synchronization of a four-dimensional energy resources system with unknown parameters , 2009 .

[29]  Baogui Xin,et al.  Projective synchronization of chaotic fractional-order energy resources demand–supply systems via linear control , 2011 .

[30]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.