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Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

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Abstract

This paper proposes a fuzzy fractional integral sliding mode control for synchronizing fractional-order dynamical systems with mismatched fractional orders. It is applied to synchronize the fractional-order modified coupled dynamos chaotic systems. Synchronization between two identical fractional order, different fractional orders, integer order and fractional-order modified coupled dynamos chaotic systems have been demonstrated. For practical applications, these derived synchronized fractional-order chaotic systems are utilized to develop a novel cryptosystem for an image encryption and decryption. Numerical simulations are provided to verify the significance of theoretical analysis.

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Acknowledgments

This work was supported by the University of Malaya HIR grant UM.C/625/1/HIR/MOHE/SC/13, Malaysia. The authors are very much thankful to the editors and anonymous reviewers for their careful reading, constructive comments and fruitful suggestions to improve this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Dindigul, Tamil Nadu, India

    P. Balasubramaniam & P. Muthukumar

  2. Faculty of Science, Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia

    K. Ratnavelu

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  1. P. Balasubramaniam
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  2. P. Muthukumar
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  3. K. Ratnavelu
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Correspondence to P. Balasubramaniam.

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Balasubramaniam, P., Muthukumar, P. & Ratnavelu, K. Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system. Nonlinear Dyn 80, 249–267 (2015). https://doi.org/10.1007/s11071-014-1865-4

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  • DOI: https://doi.org/10.1007/s11071-014-1865-4

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