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

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
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.

Vehicle Traction Control: Variable-Structure Control Approach

1991 ◽  
Vol 113 (2) ◽  
pp. 223-230 ◽  
Author(s):  
Han-Shue Tan ◽  
Yuen-Kwok Chin
Keyword(s):  
Sliding Mode ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Variable Structure ◽  
Lyapunov Stability Theory ◽  
Vehicle Model ◽  
Control Laws ◽  
Traction Control ◽  
Control Approach ◽  
Structure Control

A longitudinal one-wheel vehicle model is described for both anti-lock braking and anti-span acceleration. Based on this vehicle model, sufficient conditions for applying sliding-mode control to vehicle traction are derived via Lyapunov Stability Theory. With the understanding of these sufficient conditions, control laws are designed to control vehicle traction. Both the sufficient conditions and the control laws are verified using computer simulations.

Cluster modified projective synchronization between community networks

2015 ◽  
Vol 26 (10) ◽  
pp. 1550110 ◽  
Author(s):  
Shahed Vahedi ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Adaptive Control ◽  
Controller Design ◽  
Lyapunov Stability Theory ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Community Networks ◽  
Arbitrary Matrix ◽  
Control Gain ◽  
Modified Projective Synchronization ◽  
Matrix Scaling

Cluster modified projective synchronization of two community networks with nonidentical nodes is studied in this paper. Each network has a unique dynamics and its clusters have different parameter sets which could make their dynamics chaotic or periodic for instance. Therefore, we are dealing with varieties of dynamics in these clusters. By introducing an adaptive control gain in our controller design and using Lyapunov stability theory, we show that two community networks can reach to the synchronized state having arbitrary matrix scaling factor between corresponding nodes of the networks. Moreover, using this matrix we can observe different synchronization regimes simultaneously in each pair of corresponding nodes.

scholarly journals Generalized Projective Synchronization of Chaotic Heavy Gyroscope Systems via Sliding Rule-Based Fuzzy Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Faezeh Farivar ◽  
Mahdi Aliyari Shoorehdeli ◽  
Mohammad Ali Nekoui ◽  
Mohammad Teshnehlab
Keyword(s):  
Fuzzy Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Fuzzy Rules ◽  
Projective Synchronization ◽  
Nonlinear Controller ◽  
External Disturbances ◽  
Chaotic Motions ◽  
Rule Based ◽  
Generalized Projective Synchronization

This paper proposes the generalized projective synchronization for chaotic heavy symmetric gyroscope systems versus external disturbances via sliding rule-based fuzzy control. Because of the nonlinear terms of the gyroscope, the system exhibits complex and chaotic motions. Based on Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are attained. The fuzzy rules are directly constructed subject to a common Lyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the Lyapunov sense. The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the Eigen values of the Jacobian matrix. It is a systematic procedure for synchronization of chaotic systems. It can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. It needs only one controller to realize synchronization no matter how much dimensions the chaotic system contains, and the controller is easy to be implemented. The designed controller is robust versus model uncertainty and external disturbances. Numerical simulation results demonstrate the validity and feasibility of the proposed method.

Fuzzy Control-Based Synchronization of Fractional-Order Chaotic Systems With Input Nonlinearities

2018 ◽  
pp. 261-288 ◽  
Author(s):  
Abdesselem Boulkroune ◽  
Amina Boubellouta
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Controller Design ◽  
Variable Structure ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Fuzzy Logic Systems ◽  
Bounded Disturbances ◽  
The Stability ◽  
Fuzzy Adaptive

This chapter addresses the fuzzy adaptive controller design for the generalized projective synchronization (GPS) of incommensurate fractional-order chaotic systems with actuator nonlinearities. The considered master-slave systems are with different fractional-orders, uncertain models, unknown bounded disturbances, and non-identical form. The suggested controller includes two keys terms, namely a fuzzy adaptive control and a fractional-order variable structure control. The fuzzy logic systems are exploited for approximating the system uncertainties. A Lyapunov approach is employed for determining the parameter adaptation laws and proving the stability of the closed-loop system. At last, simulation results are given to demonstrate the validity of the proposed synchronization approach.

scholarly journals On Matrix Projective Synchronization and Inverse Matrix Projective Synchronization for Different and Identical Dimensional Discrete-Time Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Adel Ouannas ◽  
Raghib Abu-Saris
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Inverse Matrix ◽  
Projective Synchronization ◽  
Linear Dynamical Systems ◽  
New Type

The problem of matrix projective synchronization (MPS) in discrete-time chaotic systems is investigated, and a new type of discrete chaos synchronization called inverse matrix projective synchronization (IMPS) is introduced. Sufficient conditions are derived for achieving MPS and IMPS between chaotic dynamical systems in discrete-time of different and identical dimensions. Based on new control schemes, Lyapunov stability theory, and stability theory of linear dynamical systems in discrete-time, some synchronization criteria are obtained. Numerical examples and simulations are used to illustrate the use of the proposed schemes.

Modified Projective Synchronization of Chaotic Systems with Unknown Parameters

2011 ◽  
Vol 128-129 ◽  
pp. 1182-1185
Author(s):  
Min Xiu Yan ◽  
Li Ping Fan
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Adaptive Sliding Mode Control ◽  
Unknown Parameters ◽  
Response System ◽  
Uncertain Chaotic Systems ◽  
Modified Projective Synchronization

This paper proposes the modified projective synchronization of uncertain chaotic systems with unknown parameters via active adaptive sliding mode control (AASMC). The disturbances are considered both in the drive and the response system. The bounds of the disturbances are unknown. The adaptive updating laws are designed to tackle the unknown parameters. Moreover, the robustness and stability of the proposed AASMC is proved by the Lyapunov stability theory. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed scheme.

ON STABILIZING N-DIMENSIONAL CHAOTIC SYSTEMS

2003 ◽  
Vol 13 (02) ◽  
pp. 473-481 ◽  
Author(s):  
LAURENT LAVAL ◽  
NACER K. M'SIRDI
Keyword(s):  
Chaotic Systems ◽  
Controller Design ◽  
Variable Structure ◽  
Dimensional Subspace ◽  
Invariant Sets ◽  
Conic Section ◽  
Control Approach ◽  
Structure Control ◽  
Energy Consideration ◽  
And Control

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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