Artificial Cooperative Search algorithm for parameter identification of chaotic systems

Abstract

 Parameter estimation of chaotic systems is a challenging and critical topic in nonlinear science. Problem at hand is multi-dimensional and highly nonlinear thereof conventional optimization methods generally fail to extract the unknown parameters of chaotic system. In this study, Artificial Cooperative Search algorithm is put into practice for successful parameter estimation of chaotic systems and compared the parameter estimation performance of Artificial Cooperative Search with Bat, Artificial Bee Colony, Quantum behaved Particle Swarm Optimization algorithms. Parameter identification performance of each algorithm is outlined and benchmarked with several numerical simulations including Lörenz system, Duffing equation and Josephson junction. Results show that Artificial Cooperative Search algorithm outperforms other algorithms in terms of robustness and effectiveness. 

Keywords

• Artificial cooperative search, Chaotic systems, Metaheuristic algorithms, Parameter identification

References

1. Ahmadi M, Mojallali H (2012). Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems. Chaos Soliton Fract 45, 1108–1120
2. Biswambhar RA, Roy C, Papri S (2011). Parameter identification of a delay dynamical system using synchronization in presence of noise. Chaos Soliton Fract 32(4), 1278–1284.
3. Chang J, Yang Y, Liao T, Yan J (2008). Parameter identification of chaotic systems using evolutionary programming approach. Expert Syst. Appl. 35, 2074–2079.
4. Civicioglu P (2013). Artificial cooperative search algorithm for numerical optimization problems. Inform. Sciences. 229, 58–76.
5. Coelho LS, Bernert DLA (2009). An improved harmony search algorithm for synchronization of discrete-time chaotic systems. Chaos Soliton Fract 41, 2526–2532.
6. Dai D, Ma XK, Li FC, You Y (2002). An approach of parameter identification for a chaotic system based on genetic algorithm. Acta Phys Sin-Ch Ed. 11, 2459–2462.
7. Gao W, Zhang Z, Chong Y (2013). Chaotic System Parameter Identification Based on Firefly Optimization. Appl. Mech. Mater. (347-350), 3821-3826
8. Gholipour R, Khosravi A, Mojallali H (2013). Parameter Estimation of Lorenz Chaotic Dynamic System Using Bees Algorithm. International Journal of Engineering 26(3), 257-262.

9. He Q, Wang L, Liu B (2007). Parameter estimation for chaotic systems by particle swarm optimization. Chaos Soliton Fract 34, 654–61.
10. Karaboga D (2005). An idea based on honey bee swarm for numerical optimization, Technical Report-RE06, Erciyes University, Engineering Faculty, Computer Engineering Department.
11. Ko C, Fu Y, Lee C, Wu C (2010). Parameter estimation of chaotic systems by a nonlinear time-varying evolution PSO method. Artif Life Robotics 15, 33–36.
12. Li L, Yang Y, Peng H, Wang X (2006). Parameter identification of chaotic systems via chaotic ant swarm. Chaos Soliton Fract 28, 1204–1211.
13. Li C, Zhou J, Xiao J, Xiao H (2012). Parameters identification of chaotic system by chaotic gravitational search algorithm. Chaos Soliton Fract 45, 539–547.
14. Modares H, Alfi A, Fateh M (2010). Parameter identification of chaotic dynamics systems through an improved particle swarm optimization. Expert Syst Appl 37, 3714–3720.
15. Peng B, Liu B, Zhang FY, Wang L (2009). Differential evolution algorithm based parameter identification for chaotic systems. Chaos Soliton Fract 39(5), 2110–2118.
16. Rahul K (2005). Identification of all model parameters of chaotic systems from discrete scalar time series measurements. Phys Lett A 346 (4), 275–280.
17. Sun J, Feng B, Xu WB. Particle swarm optimization with particles having quantum behaviour. In: The Congress on Evolutionary Computation, IEEE Press, 2004, Portland.
18. Sun J, Zhao J, Wu X, Fang W, Cai Y, Xu W (2010). Parameter estimation for chaotic systems with a Drift Particle Swarm Optimization method. Phys Lett A 374, 2816–2822
19. Tang Y, Guan X (2009). Parameter estimation for time-delay chaotic system by particle swarm optimization. Chaos Soliton Fract 40, 1391–1398.
20. Tang Y, Guan X (2009). Parameter estimation of chaotic system with time delay: A differential evolution approach. Chaos Soliton Fract 42, 3132–3139.
21. Tien J, Li TS (2012). Hybrid Taguchi-chaos of multilevel immune and the artificial bee colony algorithm for parameter identification of chaotic systems. Comput Math Appl 64, 1108–1119.
22. Wang S, Chang Y, Li X, Zhang J (2010). Parameter identification for a class of nonlinear chaotic and hyperchaotic flows. Nonlinear Anal-Theor 11, 423-431.
23. Wang L, Xu Y (2011). An effective hybrid biogeography-based optimization algorithm for parameter estimation of chaotic systems. Expert Syst Appl 38, 15103–15109.
24. Wang L, Li L (2010). An effective hybrid quantum-inspired evolutionary algorithm for parameter estimation of chaotic systems. Expert Syst Appl 37, 1279–1285.
25. Wang L, Xu Y, Li L (2011). Parameter identification of chaotic systems by hybrid Nelder–Mead simplex search and differential evolution algorithm. Expert Syst Appl 38, 3238–3245.
26. Xiang-Tao L, Ming-Hao Y (2012). Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method. Chin Phys B 21 (5), 050507(1-6)
27. Yang K, Maginu K, Nomura H (2009). Parameters identification of chaotic systems by quantum-behaved particle swarm optimization. Int J Comput Math 86(12), 2225-2235.
28. Yang XS, A New Metaheuristic Bat-Inspired Algorithm, in: Nature Inspired Cooperative Strategies for Optimization, NISCO 2010, Studies in Computational Intelligence, Springer Berlin 284, 65–74.
29. Yeh WJ, Kao YH (1983). Intermittency in Josephson junctions. Appl. Phys. Lett 42, 1599-1602.
30. Zhou T, Chen G, Tang Y (2004). A universal unfolding of the Lorenz system. Chaos Soliton Fract 20, 979–93.