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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 1, Pages 36–47
DOI: https://doi.org/10.4213/tmf9046 (Mi tmf9046) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Chaos control and function projective synchronization of fractional-order systems through the backstepping method

S. Das, V. K. Yadav

Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, India
Full-text PDF (1300 kB) Citations (18)
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DOI: https://doi.org/10.4213/tmf9046
Abstract: We study the chaos control and the function projective synchronization of a fractional-order T-system and Lorenz chaotic system using the backstepping method. Based on stability theory, we consider the condition for the local stability of nonlinear three-dimensional commensurate fractional-order system. Using the feedback control method, we control the chaos in the considered fractional-order T-system. We simulate the function projective synchronization between the fractional-order T-system and Lorenz system numerically using MATLAB and depict the results with plots.
Keywords: fractional derivative, chaotic T-system, Lorenz system, backstepping method, feedback control method, Lyapunov stability theory, synchronization.
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 1, Pages 1430–1439
DOI: https://doi.org/10.1134/S0040577916100032
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. Das, V. K. Yadav, “Chaos control and function projective synchronization of fractional-order systems through the backstepping method”, TMF, 189:1 (2016), 36–47; Theoret. and Math. Phys., 189:1 (2016), 1430–1439
Citation in format AMSBIB
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    3. Le Zhao, Guanci Yang, Yang Li, Xuechun Hu, “Fuzzy adaptive optimal backstepping control of the FO MEMS resonator under imprecise target trajectory with disturbance compensation mechanism”, Nonlinear Dyn, 111:19 (2023), 17939  crossref
    4. Hanlin Dong, Jinde Cao, Heng Liu, “Observers-based event-triggered adaptive fuzzy backstepping synchronization of uncertain fractional order chaotic systems”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33:4 (2023)  crossref
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    6. Lixiong Lin, “Projective synchronization of two coupled Lorenz chaotic systems in predefined time”, Int. J. Dynam. Control, 10:3 (2022), 879  crossref
    7. Lixiong Lin, Yufu Zhuang, Xiafu Peng, 2022 41st Chinese Control Conference (CCC), 2022, 686  crossref
    8. Alison Garza-Alonso, Michael Basin, Pablo Rodriguez-Ramirez, 2022 16th International Workshop on Variable Structure Systems (VSS), 2022, 219  crossref
    9. Anmol Assal, Jay Prakash Singh, Binoy Krishna Roy, “Comparatively better and effective adaptive controllers for synchronisation between identical hyperchaotic systems”, IFAC-PapersOnLine, 55:1 (2022), 64  crossref
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    11. Sh. Luo, J. Li, Sh. Li, J. Hu, “Dynamical analysis of the fractional-order centrifugal flywheel governor system and its accelerated adaptive stabilization with the optimality”, Int. J. Electr. Power Energy Syst., 118 (2020), 105792  crossref  isi
    12. Luo Sh., Li Sh., Yang G., Ouakad H.M., Karami F., “Dynamical Analysis and Anti-Oscillation-Based Adaptive Control of the Fo Arch Mems With Optimality”, Nonlinear Dyn., 101:1 (2020), 293–309  crossref  isi
    13. L. Lin, “Predefined-time antisynchronization of two different chaotic neural networks”, Complexity, 2020 (2020), 7476250  crossref  isi
    14. V. K. Yadav, V. K. Shukla, S. Das, “Difference synchronization among three chaotic systems with exponential term and its chaos control”, Chaos Solitons Fractals, 124 (2019), 36–51  crossref  mathscinet  isi  scopus
    15. V. K. Yadav, V. K. Shukla, S. Das, A. Y. T. Leung, M. Srivastava, “Function projective synchronization of fractional order satellite system and its stability analysis for incommensurate case”, Chin. J. Phys., 56:2 (2018), 696–707  crossref  mathscinet  isi  scopus
    16. Sh. Luo, Sh. Li, F. Tajaddodianfar, J. Hu, “Anti-oscillation and chaos control of the fractional-order brushless DC motor system via adaptive echo state networks”, J. Frankl. Inst.-Eng. Appl. Math., 355:14 (2018), 6435–6453  crossref  mathscinet  isi  scopus
    17. S. Ahadpour, A. Nemati, F. Mirmasoudi, N. Hematpour, “Projective synchronization of piecewise nonlinear chaotic maps”, Theoret. and Math. Phys., 197:3 (2018), 1856–1864  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    18. Sh. Gao, Yu. Wang, H. Dong, B. Ning, H. Wang, “Controlling uncertain Genesio-Tesi chaotic system using adaptive dynamic surface and nonlinear feedback”, Chaos Solitons Fractals, 105 (2017), 180–188  crossref  mathscinet  zmath  isi  scopus
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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