Sliding Mode Controller Design for Global Chaos Synchronization of Coullet Systems

Vaidyanathan, Sundarapandian

doi:10.5121/ijist.2012.2207

Cited by 7 publications

(9 citation statements)

References 36 publications

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“…Among the most promising results in chaos synchronisation, are the sliding mode algorithms [11,12] since these assure fast synchronisation by enforcing a stable sliding motion in finite-time [13]. However, although finite-time stability is a desirable property, the settling-time function (the time at which the sliding mode is enforced) is generally an unbounded function with respect to initial conditions [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Single‐channel predefined‐time synchronisation of chaotic systems

Muñoz‐Vázquez

Sánchez‐Torres

Anguiano‐Gijón

2019

Asian Journal of Control

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Chaos has attracted the interest of the research community due to its applications in secure communication, and in the study of complex systems in physics, engineering and other applied sciences. In the particular case of secure communication, fast synchronisation is a requirement to avoid any loss of information at the initial stage, when the signalisation data is transmitted. With the aim of providing fast and precise synchronisation, a novel algorithm is proposed in this paper, such that, by considering just one channel of communication, a dynamic observer synchronises with a chaotic system in predefined‐time. The proposal is based on the equivalent control concept of sliding mode theory, and the stability of the synchronisation is demonstrated in the Lyapunov framework. A simulation study is carried out to highlight the reliability of the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

Single‐channel predefined‐time synchronisation of chaotic systems

Muñoz‐Vázquez

Sánchez‐Torres

Anguiano‐Gijón

2019

Asian Journal of Control

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“…Closed-loop control also includes methods such as backstepping control Rasappan and Vaidyanathan, 2012;Vaidyanathan et al, 2014, active control (Sundarapandian and Karthikeyan, 2012;Karthikeyan and Sundarapandian, 2014;Sarasu and Sundarapandian, 2011;Vaidyanathan and Rajagopal, 2011), adaptive control Vaidyanathan and Volos, 2015;Vaidyanathan et al, 2015e;Vaidyanathan and Pakiriswamy, 2015;Vaidyanathan and Azar, 2016a, 2016b, 2016c, 2016d, sliding mode control (Cao et al, 2016;Boujelben et al, 2016;Vaidyanathan and Sampath, 2012;Sundarapandian and Sivaperumal, 2011;Vaidyanathan, 2015u) and intelligent control (Boulkroune et al, 2016a(Boulkroune et al, , 2016bSadeghpour et al, 2012;Wang et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation

Vaidyanathan

Azar

Boulkroune

2018

IJAAC

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This work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. A qualitative analysis of the properties of the novel 4-D hyperchaotic system is presented. A special feature of our novel hyperchaotic system is that it has three equilibrium points of which two are unstable and one is locally asymptotically stable. The Lyapunov exponents of the novel hyperchaotic system are obtained as L1 = 1.5146, L2 = 0.2527, L3 = 0 and L4 = −12.7626. The Kaplan-Yorke dimension of the novel hyperchaotic system is derived as DKY = 3.1385. Next, this work describes the design of an adaptive controller for the global hyperchaos synchronisation of identical novel hyperchaotic systems with unknown parameters. MATLAB simulations are shown to describe all the main results derived in this work.

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“…In this example, it is assumed that Genesio-Tesi is the master system and Coullet is the slave system [13,30,35]. The master system is described previously in (47) from example and thus, we introduce the following slave dynamics:…”

Section: Example 2: Genesio-tesi and Coullet Systemsmentioning

confidence: 99%