A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 4 Issue 1
Jan.  2017

IEEE/CAA Journal of Automatica Sinica

• JCR Impact Factor: 6.171, Top 11% (SCI Q1)
CiteScore: 11.2, Top 5% (Q1)
Google Scholar h5-index: 51， TOP 8
Turn off MathJax
Article Contents
Wenjuan Gu, Yongguang Yu and Wei Hu, "Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay," IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 107-113, Jan. 2017.
 Citation: Wenjuan Gu, Yongguang Yu and Wei Hu, "Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay," IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 107-113, Jan. 2017.

# Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay

Funds:

National Natural Science Foundation of China 11371049

• It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system's parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony (ABC) algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.

•  [1] I.Podlubny, Fractional Differential Equations.San Diego:Academic Press, 1998. [2] B.Mathieu, P.Melchior, A.Oustaloup, and C.Ceyral, "Fractional differentiation for edge detection, "Signal Proc., vol.83, no.11, pp.2421-2432, Nov.2003. https://www.researchgate.net/publication/222684411_Fractional_differentiation_for_edge_detection [3] M.F.Silva, J.A.T.Machado, and A.M.Lopes, "Fractional order control of a hexapod robot, "Nonlinear Dyn., vol.38, no.1-4, pp.417-433, Dec.2004. [4] W.Chen, L.J.Ye, and H.G.Sun, "Fractional diffusion equations by the Kansa method, "Comput.Math.Appl., vol.59, no.5, pp.1614-1620, Mar.2010. http://www.sciencedirect.com/science/article/pii/S0898122109005379 [5] M.A.E.Herzallah and D.Baleanu, "Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations, "Nonlinear Dyn., vol.58, no.1-2, pp.385-391, Oct.2009. http://www.sciencedirect.com/science/article/pii/S0022247X02001804 [6] M.Lakshmanan and D.V.Senthilkumar, Dynamics of Nonlinear Time-Delay Systems.Berlin Heidelberg:Springer, 2011. [7] S.Bhalekar and V.Daftardar-Gejji, "A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order, "J. Fract.Calculus Appl., vol.1, no.5, pp.1-9, Jan.2011. https://www.researchgate.net/publication/282942655_A_Predictor-Corrector_Scheme_for_Solving_a_Nonlinear_Circuit [8] M.C.Mackey and L.Glass, "Oscillation and chaos in physiological control systems, "Science, vol.197, no.4300, pp.287-289, Jul.1977. http://science.sciencemag.org/content/197/4300/287.abstract [9] E.M.Shahverdiev and K.A.Shore, "Synchronization in multiple time delay chaotic laser diodes subject to incoherent optical feedbacks and incoherent optical injection, "Nonlinear Anal.Real World Appl., vol.12, no.6, pp.3114-3124, Dec.2011. http://www.sciencedirect.com/science/article/pii/S1468121811001064 [10] H.Wang, X.Wang, X.J.Zhu, and X.H.Wang, "Linear feedback controller design method for time-delay chaotic systems, "Nonlinear Dyn., vol.70, no.1, pp.355-362, Oct.2012. [11] Z.Wang, X.Huang, and G.D.Shi, "Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay, "Comput. Math.Appl., vol.62, no.3, pp.1531-1539, Aug.2011. https://westviewpress.com/books/nonlinear-dynamics-and-chaos/ [12] V.Daftardar-Gejji, S.Bhalekar, and P.Gade, "Dynamics of fractionalordered Chen system with delay, "Pramana,vol.79, no.1, pp.61-69, Jul.2012. https://www.researchgate.net/publication/257767557_Dynamics_of_fractional-ordered_Chen_system_with_delay [13] S.Bhalekar and V.Daftardar-Gejji, "Fractional ordered Liu system with time-delay, "Commun.Nonlinear Sci.Numer.Simul., vol.15, no.8, pp.2178-2191, Aug.2010. https://www.researchgate.net/publication/222852101_Fractional_ordered_Liu_system_with_time-delay [14] Z.M.Odibat, N.Corson, M.A.Aziz-Alaoui, and C.Bertelle, "Synchronization of chaotic fractional-order systems via linear control, "Int. J.Bifurc.Chaos, vol.20, no.1, pp.81-97, Jan.2010. http://www.sciencedirect.com/science/article/pii/S1007570409006352 [15] X.Y.Wang, X.P.Zhang, and C.Ma, "Modified projective synchronization of fractional-order chaotic systems via active sliding mode control, Nonlinear Dyn., vol.69, no.1-2, pp.511-517, Jul.2012. http://ishare.iask.sina.com.cn/f/63936585.html [16] S.Bhalekar and V.Daftardar-Gejji, "Synchronization of different fractional order chaotic systems using active control, "Commun.Nonlinear Sci.Numer.Simul., vol.15, no.11, pp.3536-3546, Nov.2010. http://www.sciencedirect.com/science/article/pii/S1007570409006352 [17] R.Konnur, "Synchronization-based approach for estimating all model parameters of chaotic systems, "Phys.Rev.E, vol.67, no.2, pp.027204, Feb.2003. http://www.docin.com/p-1178338927.html [18] N.Q.Li, W.Pan, L.S.Yan, B.Luo, M.F.Xu, N.Jiang, and Y.L.Tang, On joint identification of the feedback parameters for hyperchaotic systems:an optimization-based approach, "Chaos Solit.Fract., vol.44, no.4-5, pp.198-207, May 2011. http://www.sciencedirect.com/science/article/pii/S0960077911000142 [19] M.F.Hu, Z.Y.Xu, R.Zhang, and A.H.Hu, "Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems, "Phys.Lett.A, vol.361, no.3, pp.231-237, Jan.2007. http://www.sciencedirect.com/science/article/pii/S0375960106014630 [20] Y.G.Tang, X.Y.Zhang, C.C.Hua, L.X.Li, and Y.X.Yang, "Parameter identification of commensurate fractional-order chaotic system via differential evolution, "Phys.Lett.A, vol.376, no.4, pp.457-464, Jan.2012. http://www.docin.com/p-304422325.html [21] Y.Huang, F.Guo, Y.L.Li, and Y.F.Liu, "Parameter estimation of fractional-order chaotic systems by using quantum parallel particle swarm optimization algorithm, "PLoS One, vol.10, no.1, pp.e0114910, Jan.2015. http://www.doc88.com/p-3724514299934.html [22] Z.Sheng, J.Wang, S.D.Zhou, and B.H.Zhou"Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm, "Chaos, vol.24, no.1, pp.013133, Mar.2014. http://www.sciencedirect.com/science/article/pii/S0960077906003067 [23] J.Lin, "Parameter estimation for time-delay chaotic systems by hybrid biogeography-based optimization, "Nonlinear Dyn., vol.77, no.3, pp.983-992, Aug.2014. http://www.sciencedirect.com/science/article/pii/S0960077907007576 [24] D.Karaboga, "An idea based on honey bee swarm for numerical optimization, Tech.Rep.TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, Jan.2005. http://www.pudn.com/downloads485/doc/detail2023734.html [25] D.Karaboga and B.Akay, "A comparative study of artificial bee colony algorithm, "Appl.Math.Comput., vol.214, no.1, pp.108-132, Aug.2009. http://www.sciencedirect.com/science/article/pii/S0096300309002860 [26] D.Karaboga and B.Basturk, "On the performance of artificial bee colony (ABC) algorithm, "Appl.Soft Comput., vol.8, no.1, pp.687-697, Jan.2008. http://www.sciencedirect.com/science/article/pii/S1568494607000531 [27] K.S.Tang, K.F.Man, S.Kwong, and Q.He, "Genetic algorithms and their applications, "IEEE Signal Proc.Mag., vol.13, no.6, pp.22-37, Nov.1996. [28] K.Price, R.M.Storn, and J.A.Lampinen, Differential Evolution:A Practical Approach to Global Optimization.Berlin Heidelberg:Springer, 2005. [29] J.Kennedy, "Particle swarm optimization, "in Encyclopedia of Machine Learning, C.Sammut and G.I.Webb, Eds.US:Springer, 2010, pp.760-766.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Figures(7)  / Tables(4)