Advertisement

Parameter Estimation of Chaotic Systems Using Fireworks Algorithm

  • Hao LiEmail author
  • Peng Bai
  • Jun-Jie Xue
  • Jie Zhu
  • Hui Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9141)

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.

Keywords

Particle Swarm Optimization Chaotic System Swarm Intelligence Lorenz System Swarm Intelligence Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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) CrossRefGoogle Scholar
  2. 2.
    Zheng, S., Janecek, A., Tan, Y.: Enhanced fireworks algorithm. In: IEEE Congress on Evolutionary Computation, pp. 2069–2077. IEEE Press, Piscataway (2013)Google Scholar
  3. 3.
    Zheng, S., Janecek, A., Li, J.: Dynamic search in fireworks algorithm. In: IEEE Congress on Evolutionary Computation, pp. 3222–3229. IEEE Press, Piscataway (2014)Google Scholar
  4. 4.
    Li, J., Zheng, S., Tan, Y.: Adaptive fireworks algorithm. In: IEEE Congress on Evolutionary Computation, pp. 3214–3221. IEEE Press, Piscataway (2014)Google Scholar
  5. 5.
    Janecek, A., Tan, Y.: Swarm intelligence for non-negative matrix factorization. International Journal of Swarm Intelligence Research 2, 12–34 (2011)CrossRefGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    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) CrossRefGoogle Scholar
  8. 8.
    Wang, L., Xu, Y.: An effective hybird biogeography-based optimization algorithm for parameter estimation of chaotic sysytems. Expert Syst. Appl. 38, 15103–15109 (2011)CrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)CrossRefzbMATHGoogle Scholar
  11. 11.
    Huang, L., Feng, R., Wang, M.: Synchronization of chaotic systems via nonlinear control. Physic Letters A 320, 271–275 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Liu, Y., Wallace, K.: Modified dynamic minimization algorithm for parameter estimation of chaotic sysytem from a time series. Nonlinear Dyn. 66, 213–229 (2011)CrossRefGoogle Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    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)zbMATHGoogle Scholar
  16. 16.
    Lin, J., Xu, L.: Parameter estimation for chaotic systems based on hybrid biogeography-based optimization. Acta Phys. Sin. 62, 030505 (2013)Google Scholar
  17. 17.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Ahmadi, M., Mojallali, H.: Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems. Chaos, Solitons & Fractals 45, 1108–1120 (2012)CrossRefMathSciNetGoogle Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Lin, J., Chen, C.: Parameter estimation of chaotic systems by an oppositional seeker optimization algorithm. Nonlinear Dyn. 76, 509–517 (2014)CrossRefGoogle Scholar
  21. 21.
    He, Q., Wang, L., Liu, B.: Parameter estimation for chaotic systems by particle swarm optimization. Chaos, Solitons & Fractals 34, 654–661 (2007)CrossRefzbMATHGoogle Scholar
  22. 22.
    Peng, B., Liu, B., Zhang, F., Wang, L.: Differential evolution algorithm-based parameter estimation for chaotic systems. Chaos, Solitons & Fractals 39, 2110–2118 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hao Li
    • 1
    • 2
    Email author
  • Peng Bai
    • 1
  • Jun-Jie Xue
    • 1
  • Jie Zhu
    • 1
  • Hui Zhang
    • 2
  1. 1.Air Force Engineering UniversityXi’anChina
  2. 2.Department of IntelligenceAir Force Early-Warning AcademyWuhanChina

Personalised recommendations