Chaos Synchronization in Commensurate Fractional Order Lü System via Optimal PI λ D μ Controller with Artificial Bee Colony Algorithm

In this paper a master-slave approach to chaos synchronization in commensurate fractional order FO Lu system has been studied via optimally designed fractional order Proportional Integral Derivative PID Controller. An optimization frame work based on integral time indices has been considered for tuning the unknown parametric constants of FOPID controller. The optimization task was carried out using bees swarm intelligent based Artificial Bee Colony algorithm. A comparative study based on conventional PID control scheme has also been performed to highlight the advantage of using fractional order controller for fractional order systems. Simulation results presented for synchronization of chaos in two Lu systems supports the claim for proposed approach.

[1]  Dervis Karaboga,et al.  A comprehensive survey: artificial bee colony (ABC) algorithm and applications , 2012, Artificial Intelligence Review.

[2]  Shih-Yu Li,et al.  Generalized synchronization of chaotic systems with different orders by fuzzy logic constant controller , 2011, Expert Syst. Appl..

[3]  Simin Yu,et al.  Generating hyperchaotic Lü attractor via state feedback control , 2006 .

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

[5]  Duarte Valério,et al.  Introduction to single-input, single-output fractional control , 2011 .

[6]  I. Podlubny Fractional differential equations , 1998 .

[7]  Xu Han,et al.  Chaos Synchronization via multivariable PID Control , 2007, Int. J. Bifurc. Chaos.

[8]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[9]  I. Petráš Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[10]  Ajith Abraham,et al.  Levy mutated Artificial Bee Colony algorithm for global optimization , 2011, 2011 IEEE International Conference on Systems, Man, and Cybernetics.

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

[12]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[13]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[14]  I. Podlubny Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[15]  S. Das Functional Fractional Calculus , 2011 .

[16]  Shantanu Das,et al.  Master-slave chaos synchronization via optimal fractional order PIλDμ controller with bacterial foraging algorithm , 2012, Nonlinear Dynamics.

[17]  Mehmet Önder Efe,et al.  Fractional Order Systems in Industrial Automation—A Survey , 2011, IEEE Transactions on Industrial Informatics.

[18]  Jun-an Lu,et al.  Synchronization of a unified chaotic system and the application in secure communication , 2002 .