Chaos control and fractional inverse matrix projective difference synchronization on parallel chaotic systems with application

2022 ◽  
pp. 181-206
Author(s):  
Pushali Trikha ◽  
Lone Seth Jahanzaib ◽  
Ayub Khan
Keyword(s):  
Chaos Control ◽  
Chaotic Systems ◽  
Inverse Matrix

scholarly journals The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Runzi Luo ◽  
Haipeng Su
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Numerical Examples ◽  
Single Output ◽  
Lorenz Chaotic System ◽  
Control And Synchronization

This paper investigates the stabilization and synchronization of a class of fractional-order chaotic systems which are affected by external disturbances. The chaotic systems are assumed that only a single output can be used to design the controller. In order to design the proper controller, some observer systems are proposed. By using the observer systems some sufficient conditions for achieving chaos control and synchronization of fractional-order chaotic systems are derived. Numerical examples are presented by taking the fractional-order generalized Lorenz chaotic system as an example to show the feasibility and validity of the proposed method.

OUTPUT FEEDBACK CONTROL OF UNIFIED CHAOTIC SYSTEMS BASED ON FEEDBACK PASSIVITY

2010 ◽  
Vol 20 (05) ◽  
pp. 1519-1525 ◽  
Author(s):  
TEERAWAT SANGPET ◽  
SUWAT KUNTANAPREEDA
Keyword(s):  
Chaos Control ◽  
Chaotic Systems ◽  
Output Feedback Control ◽  
Control Law ◽  
Control Laws ◽  
Unified Chaotic Systems ◽  
System Output ◽  
Simulation Results ◽  
Passivity Based Control ◽  
System States

Recently, the concept of feedback passivity-based control has drawn attention to chaos control. In all existing papers, the implementations of passivity-based control laws require the system states for feedback. In this paper, a passivity-based control law which only requires the knowledge of the system output is proposed. Simulation results are provided to show the effectiveness of the proposed solution.

CHAOTIFICATION OF SPATIOTEMPORAL SYSTEMS

2010 ◽  
Vol 20 (07) ◽  
pp. 2193-2202 ◽  
Author(s):  
PING LI ◽  
ZHONG LI ◽  
WOLFGANG A. HALANG
Keyword(s):  
Chaos Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Spatiotemporal Chaos ◽  
Statistical Properties ◽  
Rigorous Proof ◽  
System Parameters ◽  
Simulation Results ◽  
Random Bit Generators

Spatiotemporal chaotic systems have been applied to design pseudo-random-bit generators or ciphers for better cryptographic performance, where spatiotemporal chaos is desirable. This paper presents a chaotification method (or anti-chaos control) for creating spatiotemporal systems, which are originally either nonchaotic or chaotic, strongly chaotic. Sufficient conditions on the system parameters for chaotification are obtained. A mathematically rigorous proof shows that the chaotified system satisfying the parameter conditions is chaotic in the sense of Li–Yorke and Devaney, respectively. Moreover, the chaotification method is applicable to other spatiotemporal systems even with different configurations. Simulation results have illustrated the effectiveness of the proposed chaotification method. Additionally, the statistical properties of the spatiotemporal systems and their chaotified counterparts are analyzed and compared, showing that the chaotification method endows the spatiotemporal systems with good statistical properties. Therefore, the chaotification method can be used for applications of spatiotemporal systems in cryptography.

scholarly journals Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Ibtissem Talbi ◽  
Adel Ouannas ◽  
Giuseppe Grassi ◽  
Amina-Aicha Khennaoui ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Chaotic Dynamics ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Difference Operator ◽  
Dynamic Properties ◽  
Linear Control ◽  
Control Laws ◽  
Simulation Results ◽  
Control And Synchronization ◽  
Linear Controllers

Investigating dynamic properties of discrete chaotic systems with fractional order has been receiving much attention recently. This paper provides a contribution to the topic by presenting a novel version of the fractional Grassi–Miller map, along with improved schemes for controlling and synchronizing its dynamics. By exploiting the Caputo h-difference operator, at first, the chaotic dynamics of the map are analyzed via bifurcation diagrams and phase plots. Then, a novel theorem is proved in order to stabilize the dynamics of the map at the origin by linear control laws. Additionally, two chaotic fractional Grassi–Miller maps are synchronized via linear controllers by utilizing a novel theorem based on a suitable Lyapunov function. Finally, simulation results are reported to show the effectiveness of the approach developed herein.

Combination of Improved OGY and Guiding Orbit Method for Chaos Control

2019 ◽  
Vol 23 (5) ◽  
pp. 847-855 ◽  
Author(s):  
Lingzhi Yi ◽  
Yue Liu ◽  
Wenxin Yu ◽  
◽  
◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Convergence Speed ◽  
Orbit Method ◽  
Modified Method

Chaotic systems have gathered much attention. When the OGY method is applied to control a chaotic system, chaos can be contained and target signals can be traced with satisfactory accuracy. However, the traditional control method have a low convergence speed, which may hamper the performance of the whole system. To solve this problem, the cuckoo search algorithm is used to guide the orbits of chaotic systems. Moreover, the OGY method is improved so that a chaotic system can be stabilized for different target points. Finally, the effectiveness of the proposed method is verified through several typical chaotic systems. The simulation results indicate that the modified method has a faster convergence speed and yields better performance than the traditional OGY control method.

TIME DELAYED REPETITIVE LEARNING CONTROL FOR CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (05) ◽  
pp. 1057-1065 ◽  
Author(s):  
YANXING SONG ◽  
XINGHUO YU ◽  
GUANRONG CHEN ◽  
JIAN-XIN XU ◽  
YU-PING TIAN
Keyword(s):  
Periodic Orbits ◽  
Adaptive Learning ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Learning Control ◽  
Control Technique ◽  
Unstable Periodic Orbits ◽  
Repetitive Learning ◽  
Control Principle

In this paper, a time-delayed chaos control method based on repetitive learning is proposed. A general repetitive learning control structure based on the invariant manifold of the chaotic system is given. The integration of the repetitive learning control principle and the time-delayed chaos control technique enables adaptive learning of appropriate control actions from learning cycles. In contrast to the conventional repetitive learning control, no exact knowledge (analytic representation) of the target unstable periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning. The controller effectively stabilizes the states of the continuous-time chaos on desired unstable periodic orbits. Simulations on the Duffing and Lorenz chaotic systems are provided to verify the design and analysis.

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