scholarly journals A Robust Control Method forQ-SSynchronization between Different Dimensional Integer-Order and Fractional-Order Chaotic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Adel Ouannas ◽  
Raghib Abu-Saris

A robust control approach is presented to study the problem ofQ-Ssynchronization between Integer-order and fractional-order chaotic systems with different dimensions. Based on Laplace transformation and stability theory of linear integer-order dynamical systems, a new control law is proposed to guarantee theQ-Ssynchronization betweenn-dimensional integer-order master system andm-dimensional fractional-order slave system. This paper provides further contribution to the topic ofQ-Schaos synchronization between integer-order and fractional-order systems and introduces a general control scheme that can be applied to wide classes of chaotic and hyperchaotic systems. Illustrative example and numerical simulations are used to show the effectiveness of the proposed method.

2021 ◽  
pp. 289-297
Author(s):  
Zhaohan zhang, Huiling Jin

This paper studies the synchronization control of fractional order chaotic systems based on memristor and its hardware implementation. This paper takes the complex dynamic phenomena of memristor turbidity system as the research background. Starting with the integer order memristor system, the fractional order form is derived based on the integer order turbid system, and its dynamics is deeply studied. At the same time, the turbidity phenomenon is applied to the watermark encryption algorithm, which effectively improves the confidentiality of the algorithm. Finally, in order to suppress the occurrence of turbidity, a fractional order sliding mode controller is proposed. In this paper, the sliding mode controller under the function switching control method is established, and the conditions for the parameters of the sliding mode controller are derived. Finally, the experimental results analyze the stability of the controlled system under different parameters, and give the corresponding time-domain waveform to verify the correctness of the theoretical analysis.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Kaijuan Xue ◽  
Yongbing Huangfu

This paper studies the synchronization of two different fractional-order chaotic systems through the fractional-order control method, which can ensure that the synchronization error converges to a sufficiently small compact set. Afterwards, the disturbance observer of the synchronization control scheme based on adaptive parameters is designed to predict unknown disturbances. The Lyapunov function method is used to verify the appropriateness of the disturbance observer design and the convergence of the synchronization error, and then the feasibility of the control scheme is obtained. Finally, our simulation studies verify and clarify the proposed method.


Author(s):  
Diyi Chen ◽  
Weili Zhao ◽  
Xinzhi Liu ◽  
Xiaoyi Ma

In this paper, we study the synchronization of a class of uncertain chaotic systems. Based on the sliding mode control and stability theory in fractional calculus, a new controller is designed to achieve synchronization. Examples are presented to illustrate the effectiveness of the proposed controller, like the synchronization between an integer-order system and a fraction-order system, the synchronization between two fractional-order hyperchaotic systems (FOHS) with nonidentical fractional orders, the antisynchronization between an integer-order system and a fraction-order system, the synchronization between two new nonautonomous systems. The simulation results are in good agreement with the theory analysis and it is noted that the proposed control method is of vital importance for practical system parameters are uncertain and imprecise.


Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 559 ◽  
Author(s):  
Liang Chen ◽  
Chengdai Huang ◽  
Haidong Liu ◽  
Yonghui Xia

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.


Author(s):  
Mohammad Pourmahmood Aghababa

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.


2005 ◽  
Vol 15 (08) ◽  
pp. 2457-2468 ◽  
Author(s):  
JUHNG-PERNG SU ◽  
CHUN-CHIEH WANG

This paper deals with synchronization problems of chaotic systems by applying a new adaptive variable structure control (AVSC) scheme. On the basis of Lyapunov synthesis method and Barbalat's Lemma, the proposed control law is shown to render the slave system asymptotically synchronized with the master system even though the parameters of the master system are unknown. A robust adaptive control scheme is presented to guarantee the robustness of the synchronization against bounded disturbances. Even for the case that the slave and master chaotic systems are not of the same type, the proposed AVSC may approximately null the synchronization error. We used an uncertain Rössler system, an uncertain Chua's circuit and an uncertain Duffing–Holmes oscillator as examples to illustrate the controller design. Both theoretical and simulation results strongly suggest that chaotic cryptosystems could be broken by the proposed adaptive control method. This reveals the fact that chaos-based cryptosystems may fail to achieve the secure communication.


Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Adel Ouannas ◽  
Xiong Wang ◽  
Viet-Thanh Pham ◽  
Toufik Ziar

We present new approaches to synchronize different dimensional master and slave systems described by integer order and fractional order differential equations. Based on fractional order Lyapunov approach and integer order Lyapunov stability method, effective control schemes to rigorously study the coexistence of some synchronization types between integer order and fractional order chaotic systems with different dimensions are introduced. Numerical examples are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.


2019 ◽  
Vol 14 ◽  
Author(s):  
Tayyab Khan ◽  
Karan Singh ◽  
Kamlesh C. Purohit

Background: With the growing popularity of various group communication applications such as file transfer, multimedia events, distance learning, email distribution, multiparty video conferencing and teleconferencing, multicasting seems to be a useful tool for efficient multipoint data distribution. An efficient communication technique depends on the various parameters like processing speed, buffer storage, and amount of data flow between the nodes. If data exceeds beyond the capacity of a link or node, then it introduces congestion in the network. A series of multicast congestion control algorithms have been developed, but due to the heterogeneous network environment, these approaches do not respond nor reduce congestion quickly whenever network behavior changes. Objective: Multicasting is a robust and efficient one-to-many (1: M) group transmission (communication) technique to reduced communication cost, bandwidth consumption, processing time and delays with similar reliability (dependability) as of regular unicast. This patent presents a novel and comprehensive congestion control method known as integrated multicast congestion control approach (ICMA) to reduce packet loss. Methods: The proposed mechanism is based on leave-join and flow control mechanism along with proportional integrated and derivate (PID) controller to reduce packet loss, depending on the congestion status. In the proposed approach, Proportional integrated and derivate controller computes expected incoming rate at each router and feedback this rate to upstream routers of the multicast network to stabilize their local buffer occupancy. Results: Simulation results on NS-2 exhibit the immense performance of the proposed approach in terms of delay, throughput, bandwidth utilization, and packet loss than other existing methods. Conclusion: The proposed congestion control scheme provides better bandwidth utilization and throughput than other existing approaches. Moreover, we have discussed existing congestion control schemes with their research gaps. In the future, we are planning to explore the fairness and quality of service issue in multicast communication.


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