Synchronization of fractional order Rabinovich-Fabrikant systems using sliding mode control techniques

• Autorzy: Kumar Sanjay , Singh Chaman , Prasad Sada Nand , Shekhar Chandra , Aggarwal Rajiv

Identyfikatory

DOI

10.24425/acs.2019.129384

• Języki publikacji: EN

Abstrakty

EN

In this research article, we present the concepts of fractional-order dynamical systems and synchronization methodologies of fractional order chaotic dynamical systems using slide mode control techniques. We have analysed the different phase portraits and time-series graphs of fractional order Rabinovich-Fabrikant systems. We have obtained that the lowest dimension of Rabinovich-Fabrikant system is 2.85 through utilization of the fractional calculus and computational simulation. Bifurcation diagrams and Lyapunov exponents of fractional order Rabinovich-Fabrikant system to justify the chaos in the systems. Synchronization of two identical fractional-order chaotic Rabinovich-Fabrikant systems are achieved using sliding mode control methodology.

Słowa kluczowe

EN

fractional-order chaotic system; chaos synchronization; Rabinovich-Fabrikant system; Lyapunov exponents

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 2
• Strony: 307--322
• Opis fizyczny: Bibliogr. 18 poz., rys., wykr., wzory

Twórcy

autor

Kumar Sanjay

• Department of Mathematics, Acharya Narendra Dev College (University of Delhi), Govindpuri, Kalkaji, New Delhi-110019, India

autor

Singh Chaman

• Department of Mathematics, Acharya Narendra Dev College (University of Delhi), Govindpuri, Kalkaji, New Delhi-110019, India

autor

Prasad Sada Nand

• Department of Mathematics, Acharya Narendra Dev College (University of Delhi), Govindpuri, Kalkaji, New Delhi-110019, India

autor

Shekhar Chandra

• Department of Mathematics, Deshbandhu College (University of Delhi), Kalkaji, New Delhi-110019, India

autor

Aggarwal Rajiv

• Department of Mathematics, Deshbandhu College (University of Delhi), Kalkaji, New Delhi-110019, India

Bibliografia

• [1] L. M. Pecora and T. L. Carroll: Synchronization in chaotic systems. Phys. Rev. Lett., 64 (1990), 821–824.
• [2] A. Khan and S. Kumar: Measuring chaos and synchronization of chaotic satellite systems using sliding mode control. Optimal Control, Applications and Methods (2018), DOI: 10.1002/oca.2428.
• [3] A. Khan and S. Kumar: Analysis and time-delay synchronisation of chaotic satellite systems, Pramana – J. Phys. (2018).
• [4] A. Khan and S. Kumar: Study of chaos in satellite system. Pramana –J. Phys. (2018), 90:13.
• [5] A. Khan and S. Kumar: Measure of chaos and adaptive synchronization of chaotic satellite systems, International Journal of Dynamics and Control, 2018.
• [6] I. Podlubny: Fractional differential equations. Academic Press, San Diego (CA), 1999.
• [7] S. G. Samko, A. A. Kilbas, and O. I. Marichev: Fractional integrals and derivatives: theory and applications. Gordon and Breach, Yverdon 1993.
• [8] Y. Li, Y. Chen, and I. Podlubny: Mittag-leffler stability of fractional order nonlinear dynamic systems. Automatica, 45(8) (2009), 1965–1969.
• [9] A. E. Matouk: Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system. Phys Lett. A, 373 (2009), 2166–73.
• [10] D. Y. Chen, Y. X. Liu, X. Y. Ma, and R. F. Zhang: Control of a class of fractional-order chaotic systems via sliding mode. Nonlinear Dyn., 67 (2012), 893–901.
• [11] M. R. Faieghi, H. Delavari, and D. Baleanu: A note on stability of sliding mode dynamics in suppression of fractional-order chaotic systems. Comput. Math. Appl., 66 (2013), 832–837.
• [12] M. I. Rabinovich and A. L. Fabrikant: Stochastic self-modulation of waves in nonequilibrium media. J. Exp. Theor. Phys., 77 (1979), 617–629.
• [13] M.-F. Danca, M. Fečkan, N. Kuznetsov, and G. Chen: Looking more closely to the Rabinovich-Fabrikant system. International Journal of Bifurcation and Chaos, 26(2) 1650038 (2016).
• [14] A. Khan and P. Tripathi: Synchronization Between a Fractional Order Chaotic System and an Integer Order Chaotic System, Nonlinear Dynamics and Systems Theory, 13 (4), (2013) 425–436.
• [15] M. Srivastava, S. K. Agrawal, K. Vishal, and S. Das: Chaos control of fractional order Rabinovich-Fabrikant system and synchronization between chaotic and chaos controlled fractional order Rabinovich-Fabrikant system, Appl. Math. Model., 38 (2014), 3361–3372.
• [16] V. Daftardar-Gejji and A. Babakhani: Analysis of a system of fractional differential equations. J. Math Appl Anal., 293(2) (2004), 511–522.
• [17] K. Diethelm and N. J. Ford: Analysis of fractional differential equations. J. Math Anal Appl., 265 (2002), 229–248.
• [18] G. R. Duan and H. H. Yu: LMI in control systems analysis, design and applications. CRC Press, Taylors and Francis Group, 2013.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).