Identification of Uncertain Incommensurate Fractional-Order Chaotic Systems Using an Improved Quantum-Behaved Particle Swarm Optimization Algorithm

Abstract

This paper is concerned with a significant issue in the research of nonlinear science, i.e., parameter identification of uncertain incommensurate fractional-order chaotic systems, which can be essentially formulated as a multidimensional optimization problem. Motivated by the basic particle swarm optimization and quantum mechanics theories, an improved quantum-behaved particle swarm optimization (IQPSO) algorithm is proposed to tackle this complex optimization problem. In this work, both systematic parameters and fractional derivative orders are regarded as independent unknown parameters to be identified. Numerical simulations are conducted to identify two typical incommensurate fractional-order chaotic systems. Simulation results and comparisons analyses demonstrate that the proposed method is suitable for parameter identification with advantages of high effectiveness and efficiency. Moreover, we also, respectively, investigate the effect of systematic parameters, fractional derivative orders, and additional noise on the optimization performances. The corresponding results further validate the superior searching capabilities of the proposed algorithm.