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Erschienen in:
Adaptive Sliding Mode Control of the Furuta Pendulum Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Anti-synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan–Madhavan Chaotic Systems

verfasst von : Sundarapandian Vaidyanathan, Ahmad Taher Azar

Erschienen in: Advances and Applications in Sliding Mode Control systems

Verlag: Springer International Publishing

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Abstract

Anti-synchronization is an important type of synchronization of a pair of chaotic systems called the master and slave systems. The anti-synchronization characterizes the asymptotic vanishing of the sum of the states of the master and slave systems. In other words, anti-synchronization of master and slave system is said to occur when the states of the synchronized systems have the same absolute values but opposite signs. Anti-synchronization has applications in science and engineering. This work derives a general result for the anti-synchronization of identical chaotic systems using sliding mode control. The main result has been proved using Lyapunov stability theory. Sliding mode control (SMC) is well-known as a robust approach and useful for controller design in systems with parameter uncertainties. Next, as an application of the main result, anti-synchronizing controller has been designed for Vaidyanathan–Madhavan chaotic systems (2013). The Lyapunov exponents of the Vaidyanathan–Madhavan chaotic system are found as \(L_1 = 3.2226, L_2 = 0\) and \(L_3 = -30.3406\) and the Lyapunov dimension of the novel chaotic system is found as \(D_L = 2.1095\). The maximal Lyapunov exponent of the Vaidyanathan–Madhavan chaotic system is \(L_1 = 3.2226\). As an application of the general result derived in this work, a sliding mode controller is derived for the anti-synchronization of the identical Vaidyanathan–Madhavan chaotic systems. MATLAB simulations have been provided to illustrate the qualitative properties of the novel 3-D chaotic system and the anti-synchronizer results for the identical novel 3-D chaotic systems.

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Vorheriges Kapitel Contribution to Study Performance of the Induction Motor by Sliding Mode Control and Field Oriented Control
Nächstes Kapitel Hybrid Synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan Chaotic Systems
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Metadaten
Titel
Anti-synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan–Madhavan Chaotic Systems
verfasst von
Sundarapandian Vaidyanathan
Ahmad Taher Azar
Copyright-Jahr
2015
Buch
Advances and Applications in Sliding Mode Control systems

Print ISBN: 978-3-319-11172-8

Electronic ISBN: 978-3-319-11173-5

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-11173-5_19