Parameter identification of fractional-order chaotic system with time delay via multi-selection differential evolution

In this paper, the parameter identification issue of fractional-order chaotic system with time delay is studied, which is important for its modelling and controlling. A numerical algorithm for fractional differential equation with time delay is given. Time delay and fractional order along with other ordinary parameters are estimated together, which is rarely considered before. The identification issue is converted to an optimization problem, which is nonlinear, multivariable and multimodal. To solve this complex optimization problem effectively, a multi-selection differential evolution (MS-DE) is proposed. In MS-DE, multiple vectors are generated as candidate for selection, which can avoid the local extremum and speed up the convergence speed. The simulation results illustrate the effectiveness of the proposed MS-DE method.