Anti-synchronization of four-wing chaotic systems via sliding mode control

Vaidyanathan, Sundarapandian; Sampath, Sivaperumal

doi:10.1007/s11633-012-0644-2

Cited by 133 publications

(41 citation statements)

References 21 publications

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“…In the chaos literature, an impressive variety of techniques have been proposed for chaos synchronization such as active control method [109,110,111,112,113,114,115], adaptive control method [116,117,118,119,120,121,122,123,124,125,126,127], backstepping control method [128,129,130,131,132,133,134,135], sliding mode control method [136,137,138,139,140,141,142,143,144], etc.…”

Section: Introductionmentioning

confidence: 99%

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Vaidyanathan

2017

Archives of Control Sciences

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A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control SUNDARAPANDIAN VAIDYANATHAN This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L 1 = 0.2974, L 2 = 0 and L 3 = −3.8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as D KY = 2.0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.

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Section: Introductionmentioning

confidence: 99%

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Vaidyanathan

2017

Archives of Control Sciences

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“…Various control schemes have been developed to investigate the synchronisation and anti-synchronisation problems of the chaos literature such as active control method (Ho and Hung, 2002;Chen, 2005;Karthikeyan and Sundarapandian, 2014;Sarasu and Sundarapandian, 2011;Sundarapandian and Karthikeyan, 2012a;Vaidyanathan and Rajagopal, 2011;Zhang et al, 2012), adaptive control method (Abouelsoud and Mohamed, 2015;Liao and Tsai, 2000;Sundarapandian, 2012a, 2012b;Sundarapandian and Karthikeyan, 2011a, 2011b, 2012bVaidyanathan, 2012aVaidyanathan, , 2013cPakiriswamy, 2013, 2014;Vaidyanathan et al, 2014bVaidyanathan et al, , 2015d, backstepping method (Yu and Zhang, 2004;Park, 2006;Rasappan and Vaidyanathan, 2012a, 2012b, 2014Suresh and Sundarapandian, 2013;Vaidyanathan and Rasappan, 2014;Vaidyanathan et al, 2015f), sampled-data feedback control (Zhao and Lu, 2008), time-delay feedback method (Guo and Zhong, 2009), sliding mode control (Dhanalakshmi et al, 2015;Meng et al, 2014;Rhif, 2014;Shang and Wang, 2013;Sundarapandian and Sivaperumal, 2011;Vaidyanathan, 2012bVaidyanathan, , 2012cVaidyanathan and Sampath, 2012;Vaidyanathan et al, 2015g;…”

Section: Introductionmentioning

confidence: 99%

Anti-synchronisation of identical chaotic systems via novel sliding control and its application to a novel chaotic system

Vaidyanathan

Sampath

2017

IJMIC

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This research work investigates anti-synchronisation of identical chaotic systems via a novel sliding control method. Explicitly, a general result is derived for the anti-synchronisation of identical chaotic systems using the novel sliding control method. This paper also announces a novel 3D chaotic system with four quadratic nonlinearities. The Lyapunov exponents of the novel chaotic system are obtained as L 1 = 3.7828, L 2 = 0 and L 3 = -18.7651 while the Kaplan-Yorke dimension of the novel chaotic system is obtained as D KY = 2.2016. The qualitative properties of the novel chaotic system are discussed in detail. As an application of the general control result, a sliding mode controller is derived for achieving anti-synchronisation of the identical novel chaotic systems for all initial conditions. Numerical simulations have been shown to depict the phase portraits of the novel chaotic system and the sliding mode controller design for the anti-synchronisation of identical novel chaotic systems.Keywords: chaos; chaotic systems; chaos synchronisation; anti-synchronisation; sliding mode control; Lyapunov stability theory.Reference to this paper should be made as follows: Vaidyanathan, S. and Sampath, S. (2017) 'Anti-synchronisation of identical chaotic systems via novel sliding control and its application to a novel chaotic system', Int. J. Modelling, Identification and Control, Vol. 27, No. 1, Biographical notes: Sundarapandian Vaidyanathan is a Professor and the Dean at the R&D Centre, Vel Tech University, Chennai, India. He earned his DSc in Electrical and Systems Engineering from the Washington University, St. Louis, USA in 1996. His current research focuses on linear and nonlinear control systems, chaotic and hyperchaotic systems, chaos control and synchronisation, FPGA, backstepping control, sliding mode control, mathematical models of biology, computational science and robotics. He has published over 150 Scopus-indexed research publications. He has delivered plenary lectures on control systems and chaos theory in many international conferences. He has conducted several workshops on mathematical modelling using MATLAB and SCILAB.

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“…In the chaos literature, an impressive variety of techniques have been proposed to solve the problem of chaos synchronization such as active control method [76,77], adaptive control method [78,79], backstepping control method [80,81,82,83], sliding mode control method [84,85,86,87,88,89], etc.…”

Section: Introductionmentioning

confidence: 99%

Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

Vaidyanathan¹

2016

Archives of Control Sciences

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Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system via backstepping control method SUNDARAPANDIAN VAIDYANATHAN A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained as L 1 = 0.14219, L 2 = 0.04605, L 3 = 0 and L 4 = −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as D KY = 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.

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Anti-synchronization of four-wing chaotic systems via sliding mode control

Cited by 133 publications

References 21 publications

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Anti-synchronisation of identical chaotic systems via novel sliding control and its application to a novel chaotic system

Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

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