Combination of Improved OGY and Guiding Orbit Method for Chaos Control

Lingzhi Yi; Yue Liu; Wenxin Yu

doi:10.20965/jaciii.2019.p0847

single-jc.php

« previous

JACIII Vol.23 No.5 pp. 847-855

doi: 10.20965/jaciii.2019.p0847

(2019)

Paper:

Views over last 60 days: 1,012

Combination of Improved OGY and Guiding Orbit Method for Chaos Control

Lingzhi Yi^1,2,3, Yue Liu^1,2,3,†, and Wenxin Yu^*4

^*1Hunan Province Engineering Research Center for Multi-Energy Collaborative Control Technology
Xiangtan, Hunan 411105, China

^*2Hunan Province Cooperative Innovation Center for Wind Power Equipment and Energy Conversion
Xiangtan, Hunan 411105, China

^*3College of Information Engineering, Xiangtan University
Xiangtan, Hunan 411105, China

^*4College of Electrical and Information Engineering, Hunan University
Changsha, Hunan 410082, China

^†Corresponding author

Received:

May 28, 2018

Accepted:

March 20, 2019

Published:

September 20, 2019

Keywords:

chaos control, cuckoo search (CS) algorithm, OGY, chaotic orbit guidance

Abstract

Chaotic systems have gathered much attention. When the OGY method is applied to control a chaotic system, chaos can be contained and target signals can be traced with satisfactory accuracy. However, the traditional control method have a low convergence speed, which may hamper the performance of the whole system. To solve this problem, the cuckoo search algorithm is used to guide the orbits of chaotic systems. Moreover, the OGY method is improved so that a chaotic system can be stabilized for different target points. Finally, the effectiveness of the proposed method is verified through several typical chaotic systems. The simulation results indicate that the modified method has a faster convergence speed and yields better performance than the traditional OGY control method.

Cite this article as:

L. Yi, Y. Liu, and W. Yu, “Combination of Improved OGY and Guiding Orbit Method for Chaos Control,” J. Adv. Comput. Intell. Intell. Inform., Vol.23 No.5, pp. 847-855, 2019.

Data files:

References

[1] H.-R. Lin, B.-Y. Cao, and Y.-Z. Liao, “Fuzzy Statistics and Fuzzy Probability,” Fuzzy Sets Theory Preliminary, Springer, pp. 109-134, 2018.
[2] J. C. Maxwell, “A Treatise on Electricity and Magnetism,” 3rd Edition, Vol.2, Oxford Clarendon Press, pp. 68-73, 1892.
[3] D. Xiao, J. An, M. Wu, and Y. He, “Research on Carbon-Monoxide Utilization Ratio in the Blast Furnace Based on Kolmogorov Entropy,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.2, pp. 310-316, 2016.
[4] G. Haller and T. Sapsis, “Lagrangian coherent structures and the smallest finite-time Lyapunov exponent,” Chaos: An Interdisciplinary J. of Nonlinear Science, Vol.21, No.2, Article No.023115, 2011.
[5] Y. Song, Y.-B. Li, and C.-H. Li, “Ott-Grebogi-Yorke controller design based on feedback control,” Int. Conf. on Electrical and Control Engineering, pp. 4846-4849, 2011.
[6] M. U. Akhmet and M. O. Fen, “Chaotic period-doubling and OGY control for the forced Duffing equation,” Communications in Nonlinear Science and Numerical Simulation, Vol.17, No.4, pp. 1929-1946, 2012.
[7] M.-F. Danca, “OGY method for a class of discontinuous dynamical systems,” Nonlinear Dynamics, Vol.70, No.2, pp. 1523-1534, 2012.
[8] Y. Miladi, M. Feki, and N. Derbel, “Stabilizing the unstable periodic orbits of a hybrid chaotic system using optimal control,” Communications in Nonlinear Science and Numerical Simulation, Vol.20, No.3, pp. 1043-1056, 2015.
[9] P. J. Blonigan, “New methods for sensitivity analysis of chaotic dynamical systems,” Master’s Thesis, Massachusetts Institute of Technology, 2013.
[10] Y. Sui, Y. He, W. Yu et al., “A hybrid strategy to control uncertain nonlinear chaotic system,” Chinese Physics B, Vol.26, No.10, 100503, 2017.
[11] J.-S. Wang and N.-N. Shen, “Hybrid Multiple Soft-Sensor Models of Grinding Granularity Based on Cuckoo Searching Algorithm and Hysteresis Switching Strategy,” Scientific Programming, Vol.2015, Article ID 146410, 2015.
[12] Y. Li, C. Liu, S. Zhang, W. Tan, and Y. Ding, “Reproducing Polynomial Kernel Extreme Learning Machine,” J. Adv. Comput. Intell. Intell. Inform., Vol.21, No.5, pp. 795-802, 2017.
[13] X.-S. Yang, “Cuckoo Search and Firefly Algorithm: Overview and Analysis,” Cuckoo Search and Firefly Algorithm: Theory and Applications, Splinger, pp. 1-26, 2014.
[14] W. F. H. Al-Shameri, “Dynamical properties of the Hénon mapping,” Int. J. Math. Anal., Vol.6, No.49, pp. 2419-2430, 2012.
[15] L. M. Saha and N. S. Sahni, “Chaotic evaluations in a modified coupled logistic type predator-prey model,” Applied Mathematical Sciences, Vol.6, No.139, pp. 6927-6942, 2012.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] H.-R. Lin, B.-Y. Cao, and Y.-Z. Liao, “Fuzzy Statistics and Fuzzy Probability,” Fuzzy Sets Theory Preliminary, Springer, pp. 109-134, 2018.

[2] [2] J. C. Maxwell, “A Treatise on Electricity and Magnetism,” 3rd Edition, Vol.2, Oxford Clarendon Press, pp. 68-73, 1892.

[3] [3] D. Xiao, J. An, M. Wu, and Y. He, “Research on Carbon-Monoxide Utilization Ratio in the Blast Furnace Based on Kolmogorov Entropy,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.2, pp. 310-316, 2016.

[4] [4] G. Haller and T. Sapsis, “Lagrangian coherent structures and the smallest finite-time Lyapunov exponent,” Chaos: An Interdisciplinary J. of Nonlinear Science, Vol.21, No.2, Article No.023115, 2011.

[5] [5] Y. Song, Y.-B. Li, and C.-H. Li, “Ott-Grebogi-Yorke controller design based on feedback control,” Int. Conf. on Electrical and Control Engineering, pp. 4846-4849, 2011.

[6] [6] M. U. Akhmet and M. O. Fen, “Chaotic period-doubling and OGY control for the forced Duffing equation,” Communications in Nonlinear Science and Numerical Simulation, Vol.17, No.4, pp. 1929-1946, 2012.

[7] [7] M.-F. Danca, “OGY method for a class of discontinuous dynamical systems,” Nonlinear Dynamics, Vol.70, No.2, pp. 1523-1534, 2012.

[8] [8] Y. Miladi, M. Feki, and N. Derbel, “Stabilizing the unstable periodic orbits of a hybrid chaotic system using optimal control,” Communications in Nonlinear Science and Numerical Simulation, Vol.20, No.3, pp. 1043-1056, 2015.

[9] [9] P. J. Blonigan, “New methods for sensitivity analysis of chaotic dynamical systems,” Master’s Thesis, Massachusetts Institute of Technology, 2013.

[10] [10] Y. Sui, Y. He, W. Yu et al., “A hybrid strategy to control uncertain nonlinear chaotic system,” Chinese Physics B, Vol.26, No.10, 100503, 2017.

[11] [11] J.-S. Wang and N.-N. Shen, “Hybrid Multiple Soft-Sensor Models of Grinding Granularity Based on Cuckoo Searching Algorithm and Hysteresis Switching Strategy,” Scientific Programming, Vol.2015, Article ID 146410, 2015.

[12] [12] Y. Li, C. Liu, S. Zhang, W. Tan, and Y. Ding, “Reproducing Polynomial Kernel Extreme Learning Machine,” J. Adv. Comput. Intell. Intell. Inform., Vol.21, No.5, pp. 795-802, 2017.

[13] [13] X.-S. Yang, “Cuckoo Search and Firefly Algorithm: Overview and Analysis,” Cuckoo Search and Firefly Algorithm: Theory and Applications, Splinger, pp. 1-26, 2014.

[14] [14] W. F. H. Al-Shameri, “Dynamical properties of the Hénon mapping,” Int. J. Math. Anal., Vol.6, No.49, pp. 2419-2430, 2012.

[15] [15] L. M. Saha and N. S. Sahni, “Chaotic evaluations in a modified coupled logistic type predator-prey model,” Applied Mathematical Sciences, Vol.6, No.139, pp. 6927-6942, 2012.

Combination of Improved OGY and Guiding Orbit Method for Chaos Control

Lingzhi Yi*1,*2,*3, Yue Liu*1,*2,*3,†, and Wenxin Yu*4

Lingzhi Yi^1,2,3, Yue Liu^1,2,3,†, and Wenxin Yu^*4