Non-linear Fractional-Order Chaotic Systems Identification with Approximated Fractional-Order Derivative based on a Hybrid Particle Swarm Optimization-Genetic Algorithm Method

Abstract

Although many mathematicians have searched on the fractional calculus since many years ago, but its application in engineering, especially in modeling and control, does not have many antecedents. Since there are 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 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 a N-dimensional system composed of an integrator and a phase-lead filter. A hybrid particle swarm optimization (PSO) and genetic algorithm (GA) method has been applied to estimate the parameters of approximated nonlinear fractional-order chaotic system that modeled by a state-space representation. The feasibility of this approach is demonstrated through identifying the parameters of approximated fractional-order Lorenz chaotic system. The performance of the proposed algorithm is compared with the genetic algorithm (GA) and standard particle swarm optimization (SPSO) in terms of parameter accuracy and cost function. To evaluate the identification accuracy, the time-domain output error is designed as the fitness function for parameter optimization. Simulation results show that the proposed method is more successful than other algorithms for parameter identification of fractional order chaotic systems.