ON STABILIZING N-DIMENSIONAL CHAOTIC SYSTEMS

This paper deals with the control of a class of n-dimensional chaotic systems. The proposed method consists in a Variable Structure Control approach based on system energy consideration for both controller design and system stabilization. First, we present some theoretical results related to the stabilization of global invariant sets included in a selected two-dimensional subspace of the state space. Then, we define some conditions, involving both system definition and control law design, under which the stabilized orbits can be maintained in a neighborhood of an invariant, nondegenerate, closed conic section (i.e. an ellipse or a circle). Finally, an example related to the chaotic circuit of Chua is given.

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Robust Controller Design for Modified Projective Synchronization of Chen-Lee Chaotic Systems with Nonlinear Inputs

Mathematical Problems in Engineering ◽

10.1155/2009/649401 ◽

2009 ◽

Vol 2009 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Jui-sheng Lin ◽

Neng-Sheng Pai ◽

Her-Terng Yau

Keyword(s):

Chaotic Systems ◽

Controller Design ◽

Sufficient Conditions ◽

Variable Structure ◽

Lyapunov Stability Theory ◽

Projective Synchronization ◽

Nonlinear Controller ◽

Input Nonlinearity ◽

Structure Control ◽

Modified Projective Synchronization

This study demonstrates the modified projective synchronization in Chen-Lee chaotic system. The variable structure control technology is used to design the synchronization controller with input nonlinearity. Based on Lyapunov stability theory, a nonlinear controller and some generic sufficient conditions can be obtained to guarantee the modified projective synchronization, including synchronization, antisynchronization, and projective synchronization in spite of the input nonlinearity. The numerical simulation results show that the synchronization and antisynchronization can coexist in Chen-Lee chaotic systems. It demonstrates the validity and feasibility of the proposed controller.

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Adaptive controller design for uncertain fuzzy systems using variable structure control approach

Automatica ◽

10.1016/j.automatica.2009.07.016 ◽

2009 ◽

Vol 45 (11) ◽

pp. 2646-2650 ◽

Cited By ~ 28

Author(s):

Han Ho Choi

Keyword(s):

Fuzzy Systems ◽

Controller Design ◽

Variable Structure Control ◽

Variable Structure ◽

Adaptive Controller ◽

Control Approach ◽

Structure Control

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Active queue management controller design for TCP communication networks: Variable structure control approach

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2007.07.064 ◽

2009 ◽

Vol 40 (1) ◽

pp. 277-285 ◽

Cited By ~ 15

Author(s):

Chang-Kuo Chen ◽

Teh-Lu Liao ◽

Jun-Juh Yan

Keyword(s):

Communication Networks ◽

Controller Design ◽

Active Queue Management ◽

Variable Structure Control ◽

Variable Structure ◽

Queue Management ◽

Control Approach ◽

Structure Control

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STABILIZATION OF GLOBAL INVARIANT SETS FOR CHAOTIC SYSTEMS: AN ENERGY BASED CONTROL APPROACH

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402005182 ◽

2002 ◽

Vol 12 (06) ◽

pp. 1403-1409 ◽

Cited By ~ 4

Author(s):

LAURENT LAVAL ◽

NACER K. M'SIRDI

Keyword(s):

Chaotic Systems ◽

Controller Design ◽

Sliding Mode ◽

Three Dimensional ◽

Control Design ◽

Invariant Sets ◽

Control Approach ◽

Control Objective ◽

Explicit Consideration ◽

Global Invariant

This paper presents a new control approach for steering trajectories of three-dimensional nonlinear chaotic systems towards stable stationary states or time-periodic orbits. The proposed method mainly consists in a sliding mode-based control design that is extended by an explicit consideration of system energy as basis for both controller design and system stabilization. The control objective is then to regulate the energy with respect to a shaped nominal representation implicitly related to system trajectories. In this paper, we establish some theoretical results to introduce the control design approach referred to as Energy based Sliding Mode Control (ESMC for short). Then, some capabilities of the proposed approach are illustrated through examples related to the chaotic circuit of Chua.

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