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Backstepping and Sliding Mode Control of a Fractional-Order Chaotic System

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Cybersecurity

Part of the book series: Studies in Big Data ((SBD,volume 102))

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Abstract

Fractional-order systems can come across in chemical processes, biological systems, viscoelastic systems, propagation of electromagnetic waves and electrochemical systems. In the literature, fractional systems are encountered in the modelling and controlling of such systems, synchronization applications, communication, modelling and controlling of power systems or chemical processes. Many methods such as PID, sliding mode control, backstepping control¸ fuzzy sliding mode control, model predictive control, reinforcement learning and adaptive sliding mode control, have been used in the control of such systems. In this study, a fractional-order chaotic system is proposed. For this fractional-order chaotic system, bifurcation, phase portraits and Lyapunov exponents have been calculated to investigate its chaotic status. Then, in order to control the chaotic system, mathematically backstepping and sliding mode method control laws are obtained and their applications are realised. Consequently, their system responses by means of backstepping and sliding mode control results are discussed and compared with each other. Nevertheless, both controllers successfully are be able to regulate the system by obtained control laws, even if the system is out of the chaotic situation for specified fractional-order.

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Author information

Authors and Affiliations

  1. Department of Computer Engineering, Faculty of Engineering, Hitit University, Corum, Turkey

    Akif Akgul, Omer Faruk Akmese & Hakan Kor

  2. Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University of Applied Sciences, Serdivan, Sakarya, Turkey

    Murat Erhan Cimen, Muhammed Ali Pala & Ali Fuat Boz

Authors
  1. Akif Akgul
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  2. Murat Erhan Cimen
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  3. Muhammed Ali Pala
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  4. Omer Faruk Akmese
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  5. Hakan Kor
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  6. Ali Fuat Boz
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Corresponding author

Correspondence to Akif Akgul .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shibin El Kom, Egypt

    Ahmed A. Abd El-Latif

  2. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos Volos

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Akgul, A., Cimen, M.E., Pala, M.A., Akmese, O.F., Kor, H., Boz, A.F. (2022). Backstepping and Sliding Mode Control of a Fractional-Order Chaotic System. In: Abd El-Latif, A.A., Volos, C. (eds) Cybersecurity. Studies in Big Data, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-030-92166-8_3

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