Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 4, pp. 625-634.

Voir la notice de l'article provenant de la source Library of Science

The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing–Arneodo and Duffing–Chua synchronization problems.
Keywords: chaos synchronization, adaptive control, Duffing oscillator
Mots-clés : synchronizacja chaosu, sterowanie adaptacyjne, oscylator Duffinga
@article{IJAMCS_2018_28_4_a1,
     author = {Kabzi\'nski, J.},
     title = {Synchronization of an uncertain {Duffing} oscillator with higher order chaotic systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {625--634},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2018_28_4_a1/}
}
TY  - JOUR
AU  - Kabziński, J.
TI  - Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2018
SP  - 625
EP  - 634
VL  - 28
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2018_28_4_a1/
LA  - en
ID  - IJAMCS_2018_28_4_a1
ER  - 
%0 Journal Article
%A Kabziński, J.
%T Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
%J International Journal of Applied Mathematics and Computer Science
%D 2018
%P 625-634
%V 28
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2018_28_4_a1/
%G en
%F IJAMCS_2018_28_4_a1
Kabziński, J. Synchronization of an uncertain Duffing oscillator with higher order chaotic systems. International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 4, pp. 625-634. http://geodesic.mathdoc.fr/item/IJAMCS_2018_28_4_a1/

[1] Andrievskii, B.R. and Fradkov, A.L. (2004). Control of chaos: Methods and applications. II: Applications, Automation and Remote Control 65(4): 505–533.

[2] Chang, Y., Li, X., Chu, Y. and Han, X. (2009). Synchronization of two physical systems with fully unknown parameters by adaptive control, International Workshop on Chaos-Fractals Theories and Applications, IWCFTA 2009, Shenyang, China, pp. 25–29.

[3] Dong, W., Farrell, J.A., Polycarpou, M.M., Djapic, V. and Sharma, M. (2012). Command filtered adaptive backstepping, IEEE Transactions on Control Systems Technology 20(3): 566–580.

[4] Femat, R. and Solís-Perales, G. (2002). Synchronization of chaotic systems with different order, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 65(3): 1–7.

[5] Hofmann, U., Janes, J. and Quenzer, H.J. (2012). High-Q MEMS resonators for laser beam scanning displays, Micromachines 3(2): 509–528.

[6] Hua, C. and Guan, X. (2004). Adaptive control for chaotic systems, Chaos, Solitons Fractals 22(1): 55–60.

[7] Hua, C., Guan, X. and Shi, P. (2005). Adaptive feedback control for a class of chaotic systems, Chaos, Solitons Fractals 23(3): 757–765.

[8] Ioannou, P.A. and Sun, J. (1989). Robust Adaptive Control, Dover Publications, Upper Saddle River, NJ.

[9] Kabziński, J. (2010). Adaptive control of Duffing oscillator with unknown input gain, 15th International Conference on Methods and Models in Automation and Robotics, (MMAR), Międzyzdroje, Poland, pp. 2234–2239.

[10] Kabziński, J. (2016). Adaptive tracking control of a Duffing oscillator with hard error constraints, 21st International Conference on Methods and Models in Automation and Robotics (MMAR), Międzyzdroje, Poland, pp. 1176–1181.

[11] Khalil, H.K. (2015). Nonlinear Control, Pearson Education, Upper Saddle River, NJ.

[12] Krstic, M., Kanellakopoulos, I. and Kokotovic, P. (1995). Nonlinear and Adaptive Control Design, Wiley, New York, NY.

[13] LaSalle, J.P. and Lefschetz, S. (1961). Stability by Lyapunov’s Direct Method with Applications, Academic Press, New York, NY.

[14] Pospsil, J., Kolka, Z., Horska, J. and Brzobohaty, J. (2000). Simplest ode equivalents of Chua’s equations, International Journal of Bifurcation and Chaos 10(1): 1–23.

[15] Rhoads, J.F., Shaw, S.W. and Turner, K.L. (2008). Nonlinear dynamics and its applications in microand nanoresonators, Journal of Dynamic Systems, Measurement, and Control 132(3): 1–14.

[16] Sundarapandian, V. (2010). Output regulation of the Arneodo chaotic system, ISRN Applied Mathematics 02(05): 1–11.

[17] Sundarapandian, V. (2011). Anti-synchronization of Arneodo and Coullet chaotic systems by active nonlinear control, International Journal of Control Theory and Applications 4(1): 25–36.

[18] Wang, T., Jia, N. and Zhang, F. (2015). Hybrid projective synchronization of a class of new chaotic systems, Proceedings of the 27th Chinese Control and Decision Conference, CCDC 2015, Qingdao, China, pp. 1278–1283.

[19] Wang, W. and Fan, Y. (2015). Synchronization of Arneodo chaotic system via backstepping fuzzy adaptive control, Optik 126(20): 2679–2683, DOI: 10.1016/j.ijleo.2015.06.071.

[20] Wang, X. and Mortazawi, A. (2016). Bandwidth enhancement of RF resonators using Duffing nonlinear resonance for wireless power applications, IEEE Transactions on Microwave Theory and Techniques 64(11): 3695–3702.

[21] Zhang, H., Liu, D. and Wang, Z. (2009). Controlling Chaos—Supression, Synchronization and Chaotification, Springer Verlag, London.