This paper presents the
use of active disturbance rejection control method (ADRC) to synchronize two
different chaotic systems. The master system and slave systems have
uncertainties and external disturbances. The numerical results are presented
for the synchronization between the Duffing-Holmes system and the van der pol
system. The numerical results presented show the effectiveness of the proposed
method.
References
[1]
Park, J.H., Lee, S.M. and Kwon, O.M. (2007) Adaptive Synchronization of Genesio-Tesi Chaotic System via a Novel Feedback Control. Physics Letters A, 371, 263-270.
[2]
Ahn, K. (2010) Generalized Passivity-Based Chaos Synchronization. Applied Mathematics and Mechanics, 31, 1009-1018. https://doi.org/10.1007/s10483-010-1336-6
[3]
Rodriguez, A., De Leon, J. and Fridman, L. (2007) Generalized Synchronization in Reduced-Order by Quasi-Continuous High-Order Sliding-Mode Controllers. 46th IEEE Conference on Decision and Control, New Orleans, 12-14 December 2007, 3703-3708.
[4]
Handa, H. and Sharma, B.B. (2016) Novel Adaptive Feedback Synchronization Scheme for a Class of Chaotic Systems with and without Parametric Uncertainty. Chaos, Solitons & Fractals, 86, 50-63.
[5]
Sharma, B. and Kar, I.N. (2011) Observer-Based Synchronization Scheme for a Class of Chaotic Systems Using Contraction Theory. Nonlinear Dynamics, 63, 429-445. https://doi.org/10.1007/s11071-010-9813-4
[6]
Chen, S., Hu, J., Wang, C. and Lü, J. (2004) Adaptive Synchronization of Uncertain Rössler Hyperchaotic System Based on Parameter Identification. Physics Letters A, 321, 50-55.
[7]
Yassen, M. (2005) Chaos Synchronization between Two Different Chaotic Systems Using Active Control. Chaos, Solitons & Fractals, 23, 131-140.
[8]
Khanesar, M.A., Teshnehlab, M. and Kaynak, O. (2012) Control and Synchronization of Chaotic Systems Using a Novel Indirect Model Reference Fuzzy Controller. Soft Computing, 16, 1253-1265. https://doi.org/10.1007/s00500-012-0810-z
[9]
Zhang, Z., Lu, J., Gao, L. and Shao, H. (2013) Exponential Synchronization of Genesio-Tesi Chaotic Systems with Partially Known Uncertainties and Completely Unknown Dead-Zone Nonlinearity. Journal of the Franklin Institute, 350, 347-357.
[10]
Wang, G. (2010) Stabilization and Synchronization of Genesio-Tesi System via Single Variable Feedback Controller. Physics Letters A, 374, 2831-2834.
[11]
Yadav, V.K., Mishra, P.K., Srivastava, M., Agrawal, S.K. and Mishra, V. (2016) Synchronization between Non-Autonomous Hyperchaotic Systems with Uncertainties Using Active Control Method. Procedia Computer Science, 79, 963-970.
[12]
Liu, Y. and Lee, S.M. (2016) Synchronization Criteria of Chaotic Lure Systems with Delayed Feedback PD Control. Neurocomputing, 189, 66-71.
[13]
Rodríguez, A., De León, J. and Fridman, L. (2009) Synchronization in Reduced-Order of Chaotic Systems via Control Approaches Based on High-Order Sliding-Mode Observer. Chaos, Solitons & Fractals, 42, 3219-3233.
[14]
Yahyazadeh, M., Ranjbar Noei, A. and Ghaderi, R. (2011) Synchronization of Chaotic Systems with Known and Unknown Parameters Using a Modified Active Sliding Mode Control. ISA Transactions, 50, 262-267.
[15]
Bai, E.-W. and Lonngren, K.E. (1997) Synchronization of Two Lorenz Systems Using Active Control. Chaos, Solitons & Fractals, 8, 51-58.
[16]
Lin, T.-C., Chen, M.-C. and Roopaei, M. (2011) Synchronization of Uncertain Chaotic Systems Based on Adaptive Type-2 Fuzzy Sliding Mode Control. Engineering Applications of Artificial Intelligence, 24, 39-49.
[17]
Lin, T.-C. and Kuo, C.-H. (2011) Synchronization of Uncertain Fractional Order Chaotic Systems: Adaptive Fuzzy Approach. ISA Transactions, 50, 548-556.
[18]
Feng, J., He, L., Xu, C., Austin, F. and Wu, G. (2010) Synchronizing the Noise-Perturbed Genesio Chaotic System by Sliding Mode Control. Communications in Nonlinear Science and Numerical Simulation, 15, 2546-2551.
[19]
Gao, Z. (2006) Active Disturbance Rejection Control: A Paradigm Shift in Feedback Control System Design. 2006 American Control Conference, Minneapolis, 14-16 June 2006.
[20]
Han, J. (2009) From PID to Active Disturbance Rejection Control. IEEE Transactions on Industrial Electronics, 56, 900-906. https://doi.org/10.1109/TIE.2008.2011621
[21]
Yoo, D., Yau, S.S.-T. and Gao, Z. (2007) Optimal Fast Tracking Observer Bandwidth of the Linear Extended State Observer. International Journal of Control, 80, 102-111. https://doi.org/10.1080/00207170600936555
