Synchronization of Chaotic Systems with Time Delays via Periodically Intermittent Control

2017 ◽  
Vol 26 (09) ◽  
pp. 1750139 ◽  
Author(s):  
Chao Liu ◽  
Zheng Yang ◽  
Dihua Sun ◽  
Xiaoyang Liu ◽  
Wanping Liu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Chaotic Systems ◽  
Control Period ◽  
Feasible Region ◽  
Intermittent Control ◽  
Periodically Intermittent Control ◽  
First Order ◽  
Response System ◽  
System With Time Delay

This paper investigates the exponential synchronization of chaotic systems with time delays via periodically intermittent control. Under the new differential inequality, some novel synchronization criteria are derived. In contrast to the existing works, the proposed results are less conservative because they can obtain more precise synchronized rate under the identical control conditions and remove the restrictions on the control period (or the control width) and the time delay. By using special parameters, the feasible region D(ξ), which guarantees the response system synchronizes with the drive system with synchronized rate 0.5ξ, is obtained. The Lu chaotic attractor and a first-order chaotic system with time delay are presented to demonstrate the effectiveness of the proposed results.

Adaptive Synchronization of Time-Delay Chaotic Systems with Intermittent Control

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yuangan Wang ◽  
Dong Li
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Adaptive Synchronization ◽  
Intermittent Control ◽  
Periodically Intermittent Control ◽  
Control Scheme ◽  
The Lorenz System

AbstractTime delay is a common but not negligible phenomenon in nonlinear systems, which affects the performance of synchronization. Based on principles of intermittent control and Lyapunov stability theories, we establish the synchronization criteria of the time-delay chaotic systems via adaptive intermittent control. The proposed control scheme is under aperiodically intermittent control, which is also extended to periodically intermittent control to better realization. Finally, to verify the effectiveness of our results, we choose the Lorenz system to do simulation.

SYNCHRONIZATION OF TIME-DELAYED T–S FUZZY CHAOTIC SYSTEMS VIA SCALAR OUTPUT VARIABLE

2005 ◽  
Vol 15 (08) ◽  
pp. 2593-2601 ◽  
Author(s):  
JAE-HUN KIM ◽  
HYUNSEOK SHIN ◽  
EUNTAI KIM ◽  
MIGNON PARK
Keyword(s):  
Time Delay ◽  
Fuzzy Model ◽  
Order System ◽  
Linear Matrix ◽  
Output Variable ◽  
First Order ◽  
Scalar Output ◽  
The Stability ◽  
Takagi Sugeno ◽  
System With Time Delay

It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi–Sugeno (T–S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T–S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov–Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.

scholarly journals Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Adsadang Himakalasa ◽  
Suttida Wongkaew
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Time Delays ◽  
Control Function ◽  
Discretization Method ◽  
Control Approach ◽  
First Order ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient

The Cucker and Smale model is a well-known flocking model that describes the emergence of flocks based on alignment. The first part focuses on investigating this model, including the effect of time delay and the presence of a leader. Furthermore, the control function is inserted into the dynamics of a leader to drive a group of agents to target. In the second part of this work, leadership-based optimal control is investigated. Moreover, the existence of the first-order optimality conditions for a delayed optimal control problem is discussed. Furthermore, the Runge–Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. Finally, the capacity of the proposed control approach to drive a group of agents to reach the desired places or track the trajectory is demonstrated by numerical experiment results.

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