Parameter identification and optimisation for a class of fractional-order chaotic system with time delay

Abstract

The fractional-order chaotic systems have more complex dynamic characteristics than the integer order chaotic systems, which can more reflect the physical properties of the actual system and more practical values, whereas it is difficult to control the synchronisation for fractional chaotic systems. Chaotic system identification is the basis of chaos control and performance analysis. In order to identify the parameters of the chaotic systems with time delay, a novel particle swarm optimisation with increasing inertia weight is proposed and then the issue is settled by solving an optimisation problem. The identification of parameters mainly includes the system order, the time delay parameter and the coefficient parameters. An estimation-correction algorithm based on linear interpolation method is used to solve the fractional-order delay differential equation. The Mackey-Glass chaotic system is conducted and comparisons with other two widely used particle swarm optimisations and the differential evolution algorithm indicate the effectiveness of the proposed method and an improvement in identification accuracy as well as convergence speed.