Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Fuzzy polynomial application in the synchronization of fractional order chaotic systems based on sum of squares method

Document Type : Original Article

Authors
1 Department of Electrical Engineering, Zabol Branch, Islamic Azad University, Zabol, Iran;
2 Department of Mathematics & Statics, Faculty of Basic Science, Velayat University, Iranshahr, Iran
10.22034/jfsa.2024.454601.1202
Abstract
The concept of chaos and chaotic behavior in physical and dynamic systems has received a lot of attention in recent years. Chaotic systems are systems that have nonlinear dynamic behavior and are highly sensitive to initial conditions. Analysis, control and synchronization of these systems is possible when a suitable model of them is provided first. Many non-linear systems can be modeled and controlled with the help of fuzzy logic. Takagi-Sugno fuzzy models have worked successfully for this purpose. Recently, the polynomial fuzzy technique has been proposed to generalize the T-S fuzzy model. This new model can provide a wider category of nonlinear systems. The use of fractional order calculations can lead to the efficiency of traditional control systems. Fractional order systems can provide a more accurate model of the real system. Therefore, in this research, the problem of synchronization of the fractional order system of multiple coils has been done with the help of fuzzy polynomial method. In the design of the controller, the feedback gains are obtained by the sum of squares (SOS) method. Finally, the simulation results have shown the effectiveness of the proposed polynomial fuzzy control design method.
Keywords
Subjects

[1]    Alassafi M., Ha Sh., Alsaadi F., Ahmad A. (2021) Fuzzy synchronization of fractional- order chaotic systems using finite-time command filter. Information Sciences, 579, 325-346. https://doi.org/10.1016/j.ins.2021.08.005.
 
[2]    Babanli K. M.,  Kabaoglu R. O. (2024) Synchronization of fuzzy-chaotic systems with Z-controller in secure communication. Information Sciences, 657, 119988. https://doi.org/10.1016/j.ins.2023.119988.
[3]    Chen Y. J., Chauo H. G., Wang W. J., Tsai S. H., Tanaka K., Wang H., Wang K. C. (2020) A polynomial-fuzzy-model-based synchronization methodology for the multi-scroll Chen chaotic secure communication system, Engineering Applications of Artificial Intelligence, 87, 103251, https://doi.org/10.1016/j.engappai.2019.103251.
[4]    Chen Y. J., Chou H. G., Wang. W. J. (2017) Polynomial fuzzy control design for synchronization Multi-scroll Chen Chaotic Systems. IEEE-ICASI - Meen, Prior Lam (Eds).
[5]    Chibani A., Chadli M., Benhadj N. (2016) A Sum of Squares Approach for Polynomial Fuzzy Ob- server Design for Polynomial Fuzzy Systems with Unknown Inputs. International Journal of Control, Automation and Systems, 14, 1, 323-330.
[6]    Dong H., Haung C., Cao J., Liu H. (2024) Adaptive fuzzy quantized prescribed performance synchro- nization of uncertain non-strict feedback chaotic systems with time-varying actuator failure, School of Mathematics, Southeast University, Nanjing, 211189, https://doi.org/10.1016/j.ins.2024.121241.
[7]    Feki, M. (2017) Sliding Mode Based Control and Synchronization of Chaotic Systems in Presence of Parametric Uncertainties. In: Vaidyanathan S., Lien CH. (eds) Applications of Sliding Mode Control in Science and Engineering. Studies in Computational Intelligence, 709. Springer, Cham.
[8]    Gwo-Ruey Y., Yong-Dong C., Cheng C. H. (2021) Synthesis of Polynomial Fuzzy Model-Based De- signs with Synchronization and Secure Communications for Chaos Systems with Hoo Performance. 9, 2088. https://doi.org/10.3390/pr9112088.
[9]    Hamri N., Ouahabi R. (2015) Modified projective synchronization of different chaotic systems using adaptive control. Computational and Applied Mathematics, 36, 1315-1332.
[10]        Hau Y., Fang Z., Liu H. (2024) Adaptive T-S fuzzy synchronization for uncertain fractional- order chaotic systems with input saturation and disturbance. Information Sciences, 666, 120423. https://doi.org/10.1016/j.ins.2024.120423.
[11]    Hartley T. T., Lorenzo C. F., Qammer H. K. (1995) Chaos in a fractional order Chua's system. IEEE Transaction on Circuits and Systems-1: Fundamental Theory and Applications, 42, 8.
[12]        Huang C., Cao J. (2017) Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system. Physica A, 473, 262-275.
[13]    Jiafeng Y.,Jian W., Xing W., ChunSong H., and Qinsheng L., (2019) H∞ Synchronization of Non-linear Systems Based on Polynomial Fuzzy Model, Proceedings of the 38th Chinese Control Con- ference July 27-30, Guangzhou, China, DOI:10.23919/ChiCC.2019.8865389.
 
[14]        Jiang C., Liu S., Luo C. (2014) A New Fractional-Order Chaotic Complex System and Its Antisyn- chronization. Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014.
[15]        Li C., Chen G. (2004) Chaos and hyperchaos in the fractional-order Rossler equations. Physica A, 341, 55-61.
[16]        Lin T., and Chen 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]        Lu J. G., Chen G. (2006) A note on the fractional-order Chen system. Chaos, Solitons and Fractals, 27, 685-688.
[18]        Luo C., Wang X. (2013) Chaos in the fractional-order complex Lorenz system and its synchroniza- tion. Nonlinear Dynamics, 71, 241-257.
[19]        Mingzhi J. L., Zhang M. Y. (2016) Simpler ZD-achieving controller for chaotic systems synchro- nization with parameter perturbation, model uncertainty and external disturbance as compared with other controllers. International Journal for Light and Electron Optics, 131, 364.
[20]        Mohammadzadeh A., Ghaemi S. (2015) Synchronization of chaotic systems and identification of nonlinear systems by using recurrent hierarchical type-2 fuzzy neural networks. ISA Transactions, http://dx.doi.org/10.1016/j.isatra.2015.03.016.
[21]        Muthukumar P., Balasubramaniam P., Ratnavelu K.(2016) T-S fuzzy predictive control for fractional order and its applications. Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems. Springer.
[22]        Ogunjo S. T., Ojo K. S., Fuwape I. A. (2017) Comparison of Three Different Synchronization Schemes for Fractional Chaotic Systems. Springer International Publishing AG.
[23]        Onma O.S., Njah A. N. (2014) Control and Synchronization of Chaotic and Hyperchaotic Lorenz Systems via Extended Backstepping Techniques. Hindawi Publishing Corporation Journal of Non- linear Dynamics, 2014, Article ID 861727, 15 pages.
[24]    Podlubny I. (1999) Fractional differential equations. Academic Press, New York.
[25]        Prajna S., Papachristodoulou A., Parrilo P. A. (2002) SOSTOOLS -Sum of Squares Optimization Toolbox, User's Guide. Available at http://www.cds.caltech.edu/sostools.
[26]        Sabzalian M., Mohammadzadeh A., Zhang W., Jermsittiparsert K. (2021) General type-2 fuzzy multi-switching synchronization of fractional-order chaotic systems. Engineering Applications of Artificial Intelligence, 100, 104-163. https://doi.org/10.1016/j.engappai.2021.104163.
[27]        Selvaraj P.,  Kwon O.M.,  Lee S.H.,  Sakthivel R.(2023) Robust fault-tolerant con- trol design for polynomial fuzzy systems . Fuzzy Sets and Systems, 464, 108406. https://doi.org/10.1016/j.fss.2022.09.012.
 
[28]        Senouci A., Boukabou A. (2016) Fuzzy modeling, stabilization and synchronization of multi-scroll chaotic systems.Optik 127 5351-5358.
[29]        Shao S., Chen M., Yan X. (2015) Adaptive sliding mode synchronization for a class of fractional- order chaotic systems with disturbance. Nonlinear Dynamics.
[30]        Tabasi M., Balochian S. (2018) Synchronization of the Chaotic Fractional-Order Genesio-Tesi Sys- tems Using the Adaptive Sliding Mode Fractional-Order Controller. Journal of Control, Automation and Electrical Systems, 29, 15-21.
[31]        Tanaka K., Wang H. O. (2001) Fuzzy Control Systems Design and Analysis: A Linear Matrix In- equality Approach. John Wiley Sons, Inc.
[32]        Tanaka K., Yoshida H., Wang H. O. (2009) A sum-of- squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems. IEEE Transactions on Fuzzy Systems, 17, 4.
[33]        Tirandaz H., Hajipour A. (2017) Adaptive synchronization and anti-synchronization of TSUCS and LU unified chaotic systems with unknown parameters. Optik, 130, 543-549.
[34]        Vaidyanathan S., Boulkroune, A. (2016) A Novel 4-D Hyperchaotic Chemical Reactor System and Its Adaptive Control. In: Vaidyanathan S., Volos C. (eds) Advances and Applications in Chaotic Systems. Studies in Computational Intelligence, 636. Springer, Cham.
[35]        Zhang X., Li D., Zhang X. (2017) Adaptive fuzzy impulsive synchronization of chaotic systems with random parameters. Chaos, Solitons and Fractals 104, 77-83. http://dx.doi.org/10.1016/j.chaos.2017.08.006.
[36]        Zhou S. S., Jahanshahi H., Din Q., Bekiros S., Alcaraz R., Alassafi M., Alsaadi F. E., and Chu Y. M. (2020) Discrete-time macroeconomic system: Bifurcation analysis and synchroniza- tion using fuzzy-based activation feedback control. Chaos, Solitons and Fractals 14, 110378. https://doi.org/10.1016/j.chaos.2020.110378.
[37]        Zhu Z., Zhao Z., J. Zhang, Wang R. (2020) Adaptive fuzzy control design for synchronization of chaotic time-delay system. Information Sciences, 535, 225-241. https://doi.org/10.1016/j.ins.2020.05.056.
Volume 7, Issue 1 - Serial Number 14
Open Access Statement
June 2024
Pages 163-187

  • Receive Date 28 April 2024
  • Revise Date 28 August 2024
  • Accept Date 17 September 2024