Global Chaos Synchronization of Hyperchaotic Lorenz Systems by Sliding Mode Control

Vaidyanathan, Sundarapandian; Sampath, Sivaperumal

doi:10.1007/978-3-642-24055-3_16

Cited by 58 publications

(28 citation statements)

References 23 publications

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“…Chaotic systems are characterized by prominent features such as broad Fourier transform spectra, fractal properties of the motion in phase space and extraordinary sensitivity to initial conditions and system parameter variations. The sensitivity to initial conditions is popularly known as the butterfly effect [1]. An interesting feature of chaotic systems is that the change of the parameter values can obtain different dynamical behaviors of chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Pai

2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Pai

2015

Applied Mathematics and Computation

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“…Another popular method for the synchronization of chaotic systems is the sliding mode control method [46,53,55,57,65,69,70,79,80], which is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to "slide" along a cross-section of the system's normal behavior.…”

Section: Introductionmentioning

confidence: 99%

Output Regulation of Vaidyanathan 3-D Jerk Chaotic System

Vaidyanathan

2016

Advances and Applications in Nonlinear Control Systems

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This paper investigates the problem of output regulation of the Vaidyanathan 3-D jerk chaotic system (2014). Explicitly, state feedback control laws to regulate the output of the Vaidyanathan jerk chaotic system have been derived so as to track the constant reference signals as well as to track periodic reference signals. The control laws are derived using the regulator equations of C.I. Byrnes and A. Isidori (1990), who solved the problem of output regulation of nonlinear systems involving neutrally stable exosystem dynamics. The output regulation of the Vaidyanathan jerk chaotic system has important applications in Electrical and Communication Engineering. Numerical simulations using MATLAB are shown to illustrate the phase portraits of the Vaidyanathan jerk chaotic system and the output regulation results for the Vaidyanathan jerk chaotic system.

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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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Global Chaos Synchronization of Hyperchaotic Lorenz Systems by Sliding Mode Control

Cited by 58 publications

References 23 publications

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

Output Regulation of Vaidyanathan 3-D Jerk Chaotic System

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

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