non-linear fractional-order chaotic systems identification with approximated fractional-order derivative based on a hybrid particle swarm optimization-genetic algorithm method

Although many mathematicians have searched on the fractional calculus since many years ago, its application in engineering, especially in modeling and control, does not have many antecedents. since there is much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. this paper deals with the time-domain identification fractional-order chaotic systems, where conventional derivation is replaced by a fractional one with the help of a non-integer derivation. this operator is itself approximated by an n-dimensional system composed of an integrator and a phase-lead filter. a hybrid particle swarm optimization (pso)-genetic algorithm (ga) method is applied to estimate the parameters of the approximated non-linear fractional-order chaotic system modeled by a state-space representation. the feasibility of this approach is demonstrated through identifying the parameters of the approximated fractional-order lorenz chaotic system. the performance of the proposed algorithm is compared with ga and standard particle swarm optimization (spso) in terms of parameter accuracy and cost function. in order to evaluate the identification accuracy, the time-domain output error is designed as the fitness function for parameter optimization. the simulation results show that the proposed method is more successful than the other algorithms for parameter identification of the fractional-order chaotic systems.