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Erschienen in:
Comparative Study on Fractional Order PID and PID Controllers on Noise Suppression for Manipulator Trajectory Control Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Adaptive Control of a Novel Nonlinear Double Convection Chaotic System

verfasst von : Sundarapandian Vaidyanathan, Quanmin Zhu, Ahmad Taher Azar

Erschienen in: Fractional Order Control and Synchronization of Chaotic Systems

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Control and Synchronization of Fractional-Order Chaotic Systems
Nächstes Kapitel On the Terminal Full Order Sliding Mode Control of Uncertain Chaotic Systems
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Metadaten
Titel
Adaptive Control of a Novel Nonlinear Double Convection Chaotic System
verfasst von
Sundarapandian Vaidyanathan
Quanmin Zhu
Ahmad Taher Azar
Copyright-Jahr
2017
Buch
Fractional Order Control and Synchronization of Chaotic Systems

Print ISBN: 978-3-319-50248-9

Electronic ISBN: 978-3-319-50249-6

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-50249-6_12