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Control of Shimizu–Morioka Chaotic System with Passive Control, Sliding Mode Control and Backstepping Design Methods: A Comparative Analysis

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Advances and Applications in Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 636))

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Abstract

This chapter investigates the control of continuous time Shimizu–Morioka chaotic system with unknown system parameters by means of three different control approaches, namely passive control, sliding mode control and backstepping design. Based on the properties of sliding mode control theory, the appropriate surfaces are designed. Lyapunov functions are used to realize that the passive controller and backstepping controllers ensure the global asymptotic stability of the system. Owing to the controllers, the Shimizu–Morioka chaotic system stabilizes towards its equilibrium points in the state space. Numerical simulations are performed to show and compare the efficiency of the proposed control methods.

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Author information

Authors and Affiliations

  1. Bahcelievler, Guvercin, Serdivan, Sakarya, Turkey

    Uğur Erkin Kocamaz

  2. Faculty of Engineering, Department of Electrical & Electronics Engineering, Sakarya University, Serdivan, 54187, Sakarya, Turkey

    Yilmaz Uyaroğlu

  3. Research and Development Centre, Vel Tech Dr. RR and Dr. SR Technical University, Avadi, Chennai, 600 062, Tamil Nadu, India

    Sundarapandian Vaidyanathan

Authors
  1. Uğur Erkin Kocamaz
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  2. Yilmaz Uyaroğlu
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  3. Sundarapandian Vaidyanathan
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Correspondence to Uğur Erkin Kocamaz .

Editor information

Editors and Affiliations

  1. Research and Development Centre, Vel Tech University, Chennai, India

    Sundarapandian Vaidyanathan

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

    Christos Volos

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Kocamaz, U.E., Uyaroğlu, Y., Vaidyanathan, S. (2016). Control of Shimizu–Morioka Chaotic System with Passive Control, Sliding Mode Control and Backstepping Design Methods: A Comparative Analysis. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Chaotic Systems . Studies in Computational Intelligence, vol 636. Springer, Cham. https://doi.org/10.1007/978-3-319-30279-9_17

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  • DOI: https://doi.org/10.1007/978-3-319-30279-9_17

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  • Print ISBN: 978-3-319-30278-2

  • Online ISBN: 978-3-319-30279-9

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