Chaos control and synchronization for a special generalized Lorenz canonical system – The SM system
نویسندگان
چکیده
This paper presents some simple feedback control laws to study global stabilization and global synchronization for a special chaotic system described in the generalized Lorenz canonical form (GLCF) when s = 1 (which, for convenience, we call Shimizu–Morioka system, or simply SM system). For an arbitrarily given equilibrium point, a simple feedback controller is designed to globally, exponentially stabilize the system, and reach globally exponent synchronization for two such systems. Based on the system’s coefficients and the structure of the system, simple feedback control laws and corresponding Lyapunov functions are constructed. Because all conditions are obtained explicitly in terms of algebraic expressions, they are easy to be implemented and applied to real problems. Numerical simulation results are presented to verify the theoretical predictions. 2009 Published by Elsevier Ltd.
منابع مشابه
Hybrid Control to Approach Chaos Synchronization of Uncertain DUFFING Oscillator Systems with External Disturbance
This paper proposes a hybrid control scheme for the synchronization of two chaotic Duffing oscillator system, subject to uncertainties and external disturbances. The novelty of this scheme is that the Linear Quadratic Regulation (LQR) control, Sliding Mode (SM) control and Gaussian Radial basis Function Neural Network (GRBFNN) control are combined to chaos synchronization with respect to extern...
متن کاملObserver form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization
This paper shows that a large class of chaotic systems, introduced in Celikovsky and Chen [7], as the hyperbolic-type generalized Lorenz system, can be systematically used to generate synchronized chaotic oscillations. While the generalized Lorenz system unifies the famous Lorenz system and Chen's system [10], the hyperbolic-type generalized Lorenz system is in some way complementary to it. Syn...
متن کاملHyperbolic-type Generalized Lorenz Chaotic System and Its Canonical Form
Abstract: This paper shows that a large class of chaotic systems, introduced in (Čelikovský and Vaněček, 1994), (Vaněček and Čelikovský, 1996) as the generalized Lorenz system, can be further generalized to the hyperbolic-type generalized Lorenz system. While the generalized Lorenz system unifies both the famous Lorenz system and new Chen’s system (Ueta and Chen, 1999), (Chen and Ueta, 2000), t...
متن کاملDynamical behavior and synchronization of hyperchaotic complex T-system
In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...
متن کاملDesign and Simulation of Adaptive Neuro Fuzzy Inference Based Controller for Chaotic Lorenz System
Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated....
متن کامل