Abstract
Chaotic system is a nonlinear deterministic system, and parameter identification for the chaotic system is an important issue in nonlinear science, such as secure communication, etc. By setting up an appropriate objective function, the parameter identification can be converted into a multi-dimensional optimization problem which can be solved by evolutionary algorithms. Emerging as an evolutionary algorithm, Fireworks Algorithm (FWA) has shown its good computational performance and robustness. In order to expand the application of FWA, several types of FWA are applied to estimate the parameters for two typical chaotic systems in which three parameters are totally unknown, simulation results show most of FWAs can have better estimation precision and robustness, and FWA is a new effective parameter identification method for the chaotic systems.
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References
Tan, Y., Zhu, Y.: Fireworks algorithm for optimization. In: Tan, Y., Shi, Y., Tan, K.C. (eds.) ICSI 2010, Part I. LNCS, vol. 6145, pp. 355–364. Springer, Heidelberg (2010)
Zheng, S., Janecek, A., Tan, Y.: Enhanced fireworks algorithm. In: IEEE Congress on Evolutionary Computation, pp. 2069–2077. IEEE Press, Piscataway (2013)
Zheng, S., Janecek, A., Li, J.: Dynamic search in fireworks algorithm. In: IEEE Congress on Evolutionary Computation, pp. 3222–3229. IEEE Press, Piscataway (2014)
Li, J., Zheng, S., Tan, Y.: Adaptive fireworks algorithm. In: IEEE Congress on Evolutionary Computation, pp. 3214–3221. IEEE Press, Piscataway (2014)
Janecek, A., Tan, Y.: Swarm intelligence for non-negative matrix factorization. International Journal of Swarm Intelligence Research 2, 12–34 (2011)
Zheng, S., Tan, Y.: A unified distance measure scheme for orientation coding in identification. In: International Conference on Information Science and Technology, pp. 979–985. IEEE Press, Piscataway (2013)
He, W., Mi, G., Tan, Y.: Parameter optimization of local-concentration model for spam detection by using fireworks algorithm. In: Tan, Y., Shi, Y., Mo, H. (eds.) ICSI 2013, Part I. LNCS, vol. 7928, pp. 439–450. Springer, Heidelberg (2013)
Wang, L., Xu, Y.: An effective hybird biogeography-based optimization algorithm for parameter estimation of chaotic sysytems. Expert Syst. Appl. 38, 15103–15109 (2011)
Liu, L., Zhang, J., Xu, G., Liang, L., Wang, M.: A chaotic secure communication method based on chaos systems partial series parameter estimation. Acta Phys. Sin. 63, 010501 (2014)
Hegazi, A., Agiza, H., Dessoky, M.: Adaptive Synchronization for Rossler and Chua’s Circuit Systems. International Journal of Bifurcation and Chaos 12, 1579–1597 (2002)
Huang, L., Feng, R., Wang, M.: Synchronization of chaotic systems via nonlinear control. Physic Letters A 320, 271–275 (2004)
Cheng, D., Huang, C., Cheng, S., Yan, J.: Synchronization of optical chaos in vertical-cavity surface-emitting lasers via optimal PI controller. Expert Systems with Applications 36, 6854–6858 (2009)
Liu, Y., Wallace, K.: Modified dynamic minimization algorithm for parameter estimation of chaotic sysytem from a time series. Nonlinear Dyn. 66, 213–229 (2011)
Dai, D., Ma, X., Li, F., You, Y.: An approach of parameter estimation for a chaotic system based on genetic algorithm. Acta Phys. Sin. 51, 2459–2462 (2002)
Li, L., Peng, H., Yang, Y., Wang, X.: Parameter estimation for Lorenz chaotic system based on chaotic ant swarm algorithm. Acta Phys. Sin. 56, 51–55 (2007)
Lin, J., Xu, L.: Parameter estimation for chaotic systems based on hybrid biogeography-based optimization. Acta Phys. Sin. 62, 030505 (2013)
Gao, F., Fei, F., Xu, Q., Deng, Y., Qi, Y., Balasingham, I.: A novel artifical bee colony algorithm with space contraction for unknow parameters identification and time-delays of chaotic sysytems. Applied Mathematics and Computation 219, 552–568 (2012)
Ahmadi, M., Mojallali, H.: Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems. Chaos, Solitons & Fractals 45, 1108–1120 (2012)
Sheng, Z., Wang, J., Zhou, S., Zhou, B.: Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm. CHAOS 24, 013133 (2014)
Lin, J., Chen, C.: Parameter estimation of chaotic systems by an oppositional seeker optimization algorithm. Nonlinear Dyn. 76, 509–517 (2014)
He, Q., Wang, L., Liu, B.: Parameter estimation for chaotic systems by particle swarm optimization. Chaos, Solitons & Fractals 34, 654–661 (2007)
Peng, B., Liu, B., Zhang, F., Wang, L.: Differential evolution algorithm-based parameter estimation for chaotic systems. Chaos, Solitons & Fractals 39, 2110–2118 (2009)
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Li, H., Bai, P., Xue, JJ., Zhu, J., Zhang, H. (2015). Parameter Estimation of Chaotic Systems Using Fireworks Algorithm. In: Tan, Y., Shi, Y., Buarque, F., Gelbukh, A., Das, S., Engelbrecht, A. (eds) Advances in Swarm and Computational Intelligence. ICSI 2015. Lecture Notes in Computer Science(), vol 9141. Springer, Cham. https://doi.org/10.1007/978-3-319-20472-7_49
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DOI: https://doi.org/10.1007/978-3-319-20472-7_49
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