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Comparative Study on Fractional Order PID and PID Controllers on Noise Suppression for Manipulator Trajectory Control Read chapter Read first chapter

2017 | OriginalPaper | Chapter

An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities, Its Adaptive Feedback Control and Synchronization

Authors : Sundarapandian Vaidyanathan, Ahmad Taher Azar, Adel Ouannas

Published in: Fractional Order Control and Synchronization of Chaotic Systems

Publisher: Springer International Publishing

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Abstract

This research work describes an eight-term 3-D novel polynomial chaotic system consisting of three quadratic nonlinearities. First, this work presents the 3-D dynamics of the novel chaotic system and depicts the phase portraits of the system. Next, the qualitative properties of the novel chaotic system are discussed in detail. The novel chaotic system has four equilibrium points. We show that two equilibrium points are saddle points and the other equilibrium points are saddle-foci. The Lyapunov exponents of the novel chaotic system are obtained as \(L_1 = 0.4715, L_2 = 0\) and \(L_3 = -2.4728\). The Lyapunov dimension of the novel chaotic system is obtained as \(D_{L} = 2.1907\). Next, we present the design of adaptive feedback controller for globally stabilizing the trajectories of the novel chaotic system with unknown parameters. Furthermore, we present the design of adaptive feedback controller for achieving complete synchronization of the identical novel 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 eight-term 3-D novel chaotic system.

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previous chapter A New Fractional-Order Jerk System and Its Hybrid Synchronization
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Metadata
Title
An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities, Its Adaptive Feedback Control and Synchronization
Authors
Sundarapandian Vaidyanathan
Ahmad Taher Azar
Adel Ouannas
Copyright Year
2017
Book
Fractional Order Control and Synchronization of Chaotic Systems

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

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

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-50249-6_25

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