Generalized Projective Synchronization of Three-Scroll Chaotic Systems via Active Control

Pakiriswamy, Sarasu; Vaidyanathan, Sundarapandian

doi:10.1007/978-3-642-27308-7_15

Cited by 18 publications

(17 citation statements)

References 18 publications

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“…Chaos-based applications of control systems have been devised for many engineering applications (Azar et al, 2017;Vaidyanathan and Volos, 2017). Specifically, chaos theory has applications such as jerk mechanical systems (Rasappan and Vaidyanathan, 2012;Vaidyanathan et al, 2015b;Vaidyanathan, 2015c), oscillators (Vaidyanathan et al, 2015a;Vaidyanathan, 2015f, 2015e;2012;Vaidyanathan and Rasappan, 2011;Pakiriswamy and Vaidyanathan, 2012), chemical chaotic reactor systems (Vaidyanathan, 2015b), neurons (Vaidyanathan, 2015a(Vaidyanathan, , 2015d, neural networks (Vaidyanathan, 2015g), circuits (Pham et al, 2016;Volos et al, 2017), etc. There is currently significant interest in automation and control in engineering (Thabet et al, 2017;Rakhtala and Ahmadi, 2017;Roy et al, 2017;Guo and Dong, 2017;Kiddee et al, 2017;He et al, 2017;Sarangi et al, 2017;Perumal and Gnanambal, 2017;Bennassar et al, 2017;Vaidyanathan et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

A new three-dimensional chaotic system: its adaptive control and circuit design

Vaidyanathan

Abba

Betchewe

et al. 2019

IJAAC

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A new three-dimensional chaotic system with two nonlinearities is proposed in this research work. Specifically, the two nonlinearities considered in the construction of the new chaotic system are a quadratic nonlinearity and a quartic nonlinearity. A systematic study of the three-dimensional chaotic system has been made including phase portraits, dissipativity, rest points and their stability, Lyapunov chaos exponents, Kaplan-Yorke fractal dimension, etc. As main control results, we design feedback control laws using adaptive control theory to achieve global stabilisation of the new chaotic system and also global synchronisation of identical chaotic systems with unknown parameters. Finally, an electronic circuit design of the new chaotic system using electronic work bench (EWB) is described in detail to confirm the feasibility of the theoretical chaotic model.

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Section: Introductionmentioning

confidence: 99%

A new three-dimensional chaotic system: its adaptive control and circuit design

Vaidyanathan

Abba

Betchewe

et al. 2019

IJAAC

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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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“…In the chaos literature, many different methodologies have been also proposed for the synchronization and antisynchronization of chaotic systems such as PC method [114], active control [115][116][117][118][119][120][121][122][123][124][125], time-delayed feedback control [126,127], adaptive control [128][129][130][131][132][133][134][135][136][137][138][139], sampled-data feedback control [140][141][142], backstepping control [143][144][145][146][147][148][149], sliding mode control [150][151][152][153][154][155][156][157][158], etc.…”

Section: Introductionmentioning

confidence: 99%

Analysis, Control, Synchronization and SPICE Implementation of a Novel 4 - D Hyperchaotic Rikitake Dynamo System without Equilibrium

Vaidyanathan¹,

Volos²,

Pham³

2015

JESTR

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Chaos theory has wide applications and its importance can be seen by the voluminous publications on various applications in several branches of science, commerce and engineering. Control, tracking or regulation and synchronization of different types of chaotic systems are importance areas of research in the control literature and various methods have been adopted over the past few decades for tackling these research problems. Also, the discovery of novel chaotic and hyperchaotic systems in various applications, their qualitative properties and the control of such systems are also important research areas in chaos theory. This paper announces a novel 4-D hyperchaotic Rikitake dynamo system, which is derived by adding a state feedback control to the famous 3-D Rikitake two-disk dynamo system (1958). The frequent and irregular reversals of the Earth's magnetic field inspired a number of early studies involving electrical currents within the Earth's molten core. One of the first such models to exhibit reversals was Rikitake's two-disk dynamo system (Rikitake, 1958). This paper discusses the qualitative properties of the novel hyperchaotic Rikitake dynamo system. We note that the novel hyperchaotic Rikitake dynamo system has no equilibrium points. The Lyapunov exponents of the hyperchaotic Rikitake dynamo system are found as ! = 0.09136, ! = 0.02198, ! = 0 and ! = −2.11190. The Kaplan-Yorke fractional dimension of the novel hyperchaotic Rikitake dynamo system is found as !" = 3.05367. Next, this paper discusses control and synchronization of the novel hyperchaotic Rikitake dynamo system with unknown parameters using adaptive control method. The main results are established using Lyapunov stability theory and numerically illustrated using MATLAB. Finally, for the 4-D novel hyperchaotic system, an electronic circuit realization in SPICE has been described to confirm the feasibility of the theoretical hyperchaotic Rikitake dynamo model.

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Generalized Projective Synchronization of Three-Scroll Chaotic Systems via Active Control

Cited by 18 publications

References 18 publications

A new three-dimensional chaotic system: its adaptive control and circuit design

A new three-dimensional chaotic system: its adaptive control and circuit design

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

Analysis, Control, Synchronization and SPICE Implementation of a Novel 4 - D Hyperchaotic Rikitake Dynamo System without Equilibrium

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