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Adaptive Control of a Novel Nonlinear Double Convection Chaotic System

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Fractional Order Control and Synchronization of Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 688))

Abstract

This research work describes a six-term novel nonlinear double convection chaotic system with two nonlinearities. First, this work presents the 3-D dynamics of the novel nonlinear double convection chaotic system and depicts the phase portraits of the system. Our novel nonlinear double convection chaotic system is obtained by modifying the dynamics of the Rucklidge chaotic system (1992). Next, the qualitative properties of the novel chaotic system are discussed in detail. The novel chaotic system has three equilibrium points. We show that the equilibrium point at the origin is a saddle point, while the other two equilibrium points are saddle-foci. The Lyapunov exponents of the novel nonlinear double convection chaotic system are obtained as \(L_1 = 0.2089\), \(L_2 = 0\) and \(L_3 = -3.2123\). The Lyapunov dimension of the novel chaotic system is obtained as \(D_{L} = 2.0650\). Next, we present the design of adaptive feedback controller for globally stabilizing the trajectories of the novel nonlinear double convection chaotic system with unknown parameters. Furthermore, we present the design of adaptive feedback controller for achieving complete synchronization of the identical novel nonlinear double convection chaotic systems with unknown parameters. The main adaptive control results are proved using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work for the novel nonlinear double convection system.

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Authors and Affiliations

  1. Research and Development Centre, Vel Tech University, Avadi, Chennai, 600062, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  2. Department of Engineering Design and Mathematics, University of the West of England, Bristol, UK

    Quanmin Zhu

  3. Faculty of Computers and Information, Benha University, Banha, Egypt

    Ahmad Taher Azar

  4. Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt

    Ahmad Taher Azar

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  1. Sundarapandian Vaidyanathan
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  2. Quanmin Zhu
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  3. Ahmad Taher Azar
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Correspondence to Sundarapandian Vaidyanathan .

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Editors and Affiliations

  1. Faculty of Computers and Information, Benha University Faculty of Computers and Information, AND Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt. , Benha, Egypt

    Ahmad Taher Azar

  2. Research and Development Centre, Vel Tech University Research and Development Centre, Chennai, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  3. Department of Mathematics and CS, University of Tebessa Department of Mathematics and CS, Tebessa, Algeria

    Adel Ouannas

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Vaidyanathan, S., Zhu, Q., Azar, A.T. (2017). Adaptive Control of a Novel Nonlinear Double Convection Chaotic System. In: Azar, A., Vaidyanathan, S., Ouannas, A. (eds) Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol 688. Springer, Cham. https://doi.org/10.1007/978-3-319-50249-6_12

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