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Research Papers

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

[+] Author and Article Information
Jiamin Wei

Department of Mathematics,
Beijing Jiaotong University,
Beijing 100044, China
e-mail: 16118414@bjtu.edu.cn

Yongguang Yu

Department of Mathematics,
Beijing Jiaotong University,
Beijing 100044, China
e-mail: ygyu@bjtu.edu.cn

Di Cai

Department of Mathematics,
Beijing Jiaotong University,
Beijing 100044, China
e-mail: 16121602@bjtu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 14, 2017; final manuscript received March 6, 2018; published online March 28, 2018. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 13(5), 051004 (Mar 28, 2018) (12 pages) Paper No: CND-17-1500; doi: 10.1115/1.4039582 History: Received November 14, 2017; Revised March 06, 2018

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.

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Figures

Grahic Jump Location
Fig. 1

The objective function of fractional-order financial system (20)

Grahic Jump Location
Fig. 2

Evolution process of the estimated parameters for fractional-order financial system (20): (a) evolution process of a, (b) evolution process of b, (c) evolution process of c, (d) evolution process of q1, (e) evolution process of q2, and (f) evolution process of q3

Grahic Jump Location
Fig. 3

Evolution process of objective function values for fractional-order financial system (20)

Grahic Jump Location
Fig. 4

The objective function of fractional-order Rössler system (23)

Grahic Jump Location
Fig. 5

Evolution process of the estimated parameters for fractional-order Rössler system (23): (a) evolution process of a, (b) evolution process of b, (c) evolution process of c, (d) evolution process of q1, (e) evolution process of q2, and (f) evolution process of q3

Grahic Jump Location
Fig. 6

Evolution process of objective function values for fractional-order Rössler system (23)

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