scholarly journals Active Control Design for the Hybrid Synchronization of Arneodo and Rossler Chaotic Systems

2012 ◽  
Vol 2 (2) ◽  
pp. 13-25
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Control Design ◽  
Hybrid Synchronization

Hybrid Synchronization of Lu and Bhalekar-Gejji Chaotic Systems Using Nonlinear Active Control

2014 ◽  
Vol 47 (1) ◽  
pp. 292-296 ◽  
Author(s):  
Jay Prakash Singh ◽  
Piyush Pratap Singh ◽  
B.K. Roy
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Hybrid Synchronization

Hybrid Synchronization Between 5-th Order Hyperchaotic Chua Systems

2015 ◽  
Vol 13 (1-2) ◽  
pp. 25-34
Author(s):  
Dragomir Chantov
Keyword(s):  
Active Control ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Lyapunov Method ◽  
Chaotic Synchronization ◽  
Synchronization System ◽  
Hybrid Synchronization ◽  
The Stability ◽  
Chaotic Secure Communication ◽  
Fifth Order

Abstract The aim of this paper is the design of a chaotic synchronization system with a special type of synchronization, called hybrid synchronization, on the basis of Chua’s fifth-order hyperchaotic model. When two chaotic systems are in hybrid synchronization, some of the systems’ variables pairs are in identical synchronization, and the rest are anti-synchronized. Hybrid synchronization schemes have advantages regarding the degree of signal protection, when they are used to build a chaotic secure communication system. The design of the system is accomplished by means of active control, where the Second Lyapunov method is used to prove the stability of the synchronization system.

scholarly journals Design and Implementation of a Microcontroller Based Active Controller for the Synchronization of the Petrzela Chaotic System

Computation ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 40
Author(s):  
Rivera-Blas ◽  
Paredes ◽  
Flores-Herrera ◽  
Romero
Keyword(s):  
Applied Sciences ◽  
Active Control ◽  
Chaotic Systems ◽  
A Priori ◽  
Control Design ◽  
Control Law ◽  
Chaotic Dynamical System ◽  
Digital Oscilloscope ◽  
Digital Devices ◽  
Design And Implementation

This paper presents an active control design for the synchronization of two identical Petrzela chaotic systems (Petrzela, J.; Gotthans, T. New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure. Applied Sciences. 2017, 7, 976) on master-slave configuration. For the active control, the parameters of both systems are assumed to be a priori known, the control law by means of the dynamic of the error synchronization is designed to guarantee the convergence to zero of error states and the synchronization process is verified by numerical simulation. By taking advantage of the execution and implementation facilities of microcontroller based chaotic systems in digital devices, the active controller is implemented in a 32 bits ARM microcontroller. The experimental results were obtained by using the fourth order Runge-Kutta numerical method to integrate the differential equations of the controller, where the results were measured with a digital oscilloscope.

scholarly journals Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

2014 ◽  
Vol 65 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rajagopal Karthikeyan ◽  
Vaidyanathan Sundarapandian
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Hybrid Synchronization ◽  
Active Control Method

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

Nonlinear Active Control Based Hybrid Synchronization between Hyperchaotic and Chaotic Systems

2014 ◽  
Vol 47 (1) ◽  
pp. 287-291 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Jay Prakash Singh ◽  
B.K. Roy
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Hybrid Synchronization

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

scholarly journals Observer-Based H ∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Kuan-Yi Lin ◽  
Tung-Sheng Chiang ◽  
Chian-Song Chiu ◽  
Wen-Fong Hu ◽  
Peter Liu
Keyword(s):  
Continuous Time ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Control Design ◽  
Practical Consideration ◽  
Time Varying ◽  
Fuzzy Observer ◽  
Output Tracking ◽  
Output Tracking Control

Tracking control for the output using an observer-based H ∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbances, and immeasurable states. Then, to facilitate a uniform control design approach for both discrete- and continuous-time chaotic systems, the dynamic models along with time-varying delays and disturbances are reformulated using the T-S (Takagi–Sugeno) fuzzy representation. For control design considering immeasurable states, a fuzzy observer achieves master-slave synchronization. Third, combining both a fuzzy observer for state estimation and a controller (solved from generalized kinematic constraints) output tracking can be achieved. To make the design more practical, we also consider differences of antecedent variables between the plant, observer, and controller. Finally, using Lyapunov’s stability approach, the results are sufficient conditions represented as LMIs (linear matrix inequalities). The contributions of the method proposed are threefold: (i) systemic and unified problem formulation of master-slave synchronization and tracking control for both discrete and continuous chaotic systems; (ii) practical consideration of time-varying delay, immeasurable state, different antecedent variables (of plant, observer, and controller), and disturbance in the control problem; and (iii) sufficient conditions from Lyapunov’s stability analysis represented as LMIs which are numerically solvable observer and controller gains from LMIs. We carry out numerical simulations on a chaotic three-dimensional discrete-time system and continuous-time Chua’s circuit. Satisfactory numerical results further show the validity of the theoretical derivations.

Sign in / Sign up

Export Citation Format

Share Document