Adaptive Finite-Time Synchronization of Non-Autonomous Chaotic Systems With Uncertainty

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa ◽  
Hasan Pourmahmood Aghababa
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
The State ◽  
Control Technique ◽  
Model Uncertainties ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Time Control ◽  
Engineering Sciences

Due to its useful applications in real world processes, synchronization of chaotic systems has attracted the attention of many researchers of mathematics, physics and engineering sciences. In practical situations, many chaotic systems are inevitably disturbed by model uncertainties and external disturbances. Furthermore, in practice, it is hard to determine the precise values of the chaotic systems’ parameters in advance. Besides, from a practical point of view, it is more desirable to achieve synchronization in a given finite time. In this paper, we investigate the problem of finite-time chaos synchronization between two different chaotic systems in the presence of model uncertainties, external disturbances and unknown parameters. Both autonomous and non-autonomous chaotic systems are taken into account. To tackle the unknown parameters, appropriate adaptation laws are proposed. Using the adaptation laws and finite-time control technique, an adaptive robust finite-time controller is designed to guarantee that the state trajectories slave system converge to the state trajectories of the master system in a given finite time. Some numerical simulations are presented to verify the robustness and usefulness of the proposed finite-time control technique.

Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control

2017 ◽  
Vol 24 (17) ◽  
pp. 3842-3854 ◽  
Author(s):  
Xiaojian Xi ◽  
Saleh Mobayen ◽  
Haipeng Ren ◽  
Sajad Jafari
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Control Method ◽  
Sliding Mode ◽  
Control Technique ◽  
Dimensional System ◽  
Time Control ◽  
Wide Range ◽  
Chattering Free

This paper proposes an adaptive robust finite-time control method based on a global sliding surface for the synchronization of a class of chaotic systems. New chattering-free control laws are designed to guarantee the removal of the reaching mode and realize the existence of the sliding mode around the designed surface right from the first moment. The proposed adaptive-tuning controllers eliminate the requirement of knowledge about disturbance bounds. Using the suggested control technique, superior master–slave synchronization is achieved, the chattering problem is fully solved, and the amplitudes of the control signals are noticeably decreased. Demonstrative simulation results for a Lü chaotic system are presented to indicate the efficiency and usefulness of the proposed scheme. In the end, using a state-feedback controller, we obtain a four-dimensional system with two interesting features. First, some hyperchaotic solutions are proposed, and then a continuous bifurcation diagram showing chaos for a wide range of bifurcation parameter is presented.

scholarly journals Improved Sliding Mode Finite-Time Synchronization of Chaotic Systems with Unknown Parameters

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 346
Author(s):  
Hao Jia ◽  
Chen Guo ◽  
Lina Zhao ◽  
Zhao Xu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Control Method ◽  
Sliding Mode ◽  
Unknown Parameters ◽  
Finite Time Convergence ◽  
Time Control ◽  
Adaptive Sliding Mode Controller ◽  
Terminal Sliding Surface

This work uses the sliding mode control method to conduct the finite-time synchronization of chaotic systems. The utilized parameter selection principle differs from conventional methods. The designed controller selects the unknown parameters independently from the system model. These parameters enable tracking and prediction of the additional variables that affect the chaotic motion but are difficult to measure. Consequently, the proposed approach avoids the limitations of selecting the unknown parameters that are challenging to measure or modeling the parameters solely within the relevant system. This paper proposes a novel nonsingular terminal sliding surface and demonstrates its finite-time convergence. Then, the adaptive law of unknown parameters is presented. Next, the adaptive sliding mode controller based on the finite-time control idea is proposed, and its finite-time convergence and stability are discussed. Finally, the paper presents numerical simulations of chaotic systems with either the same or different structures, thus verifying the proposed method’s applicability and effectiveness.

scholarly journals Finite–Time Adaptive Modified Function Projective Multi–Lag Generalized Compound Synchronization for Multiple Uncertain Chaotic Systems

2018 ◽  
Vol 28 (4) ◽  
pp. 613-624
Author(s):  
Qiaoping Li ◽  
Sanyang Liu ◽  
Yonggang Chen
Keyword(s):  
Adaptive Control ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Control Technique ◽  
Unknown Parameters ◽  
Theoretical Derivation ◽  
Finite Time Stability ◽  
Compound Synchronization ◽  
Different Chaotic Systems

Abstract In this paper, for multiple different chaotic systems with fully unknown parameters, a novel synchronization scheme called ‘modified function projective multi-lag generalized compound synchronization’ is put forward. As an advantage of the new method, not only the addition and subtraction, but also the multiplication of multiple chaotic systems are taken into consideration. This makes the signal hidden channels more abundant and the signal hidden methods more flexible. By virtue of finite-time stability theory and an adaptive control technique, a finite-time adaptive control scheme is established to realize the finite-time synchronization and to properly evaluate the unknown parameters. A detailed theoretical derivation and a specific numerical simulation demonstrate the feasibility and validity of the advanced scheme.

scholarly journals Finite-Time Synchronization and Identification between Two Nonlinear Coupled Multiweighted Markovian Switching Delayed Networks with Uncertain Models and External Disturbances

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Xiaofei Chen ◽  
Haifeng Qiu ◽  
Chong Xu ◽  
Zhipeng Sun
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Network Models ◽  
Markovian Switching ◽  
Model Uncertainties ◽  
External Disturbances ◽  
Multiple Weights ◽  
Adaptive Laws ◽  
True Values

In this paper, two different nonlinear coupled Markovian switching delayed network models with multiple weights are established, and the effects of parameter and model uncertainties and external disturbances are fully considered. Firstly, based on the finite-time theory, several sufficient conditions for the finite-time synchronization of Markovian switching networks are obtained. Secondly, under the feedback controller with adaptive laws, when the synchronization of the networks is achieved in a finite time, the uncertain parameters of the networks can also be identified as true values. Finally, a representative numerical simulation is given to further illustrate the validity and practicability of the theoretical analysis and proof of this paper.

Finite Time Synchronization of Chaotic Systems Without Linear Term and Its Application in Secure Communication

2021 ◽  
Vol 15 (4) ◽  
pp. 54-78
Author(s):  
Shuru Liu ◽  
Zhanlei Shang ◽  
Junwei Lei
Keyword(s):  
Finite Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Difficult Problem ◽  
Stable System ◽  
Convergence Time ◽  
Unknown Parameters ◽  
Communication Scheme ◽  
Definition Of

A definition of finite time synchronization of chaotic system was proposed, and a special theorem was proposed to solve the difficult problem of constructing a finite time stable system. After that, a hybrid construction method was proposed by integrating a common stable system and a finite time stable system. That reveals how to construct a finite time stable system, and it is very useful in secure communication since the convergence time is a very important factor that will affect its application in engineering realization. Above theorem and method was applied in the chaotic synchronization and two kinds of synchronization methods were proposed with estimation of unknown parameters. At last, a secure communication scheme was constructed by using above finite time synchronous method of chaotic systems. Also, numerical simulation was done, and the rightness of all the above proposed theorems and methods was shown.

scholarly journals Dual-stage adaptive finite-time modified function projective multi-lag combined synchronization for multiple uncertain chaotic systems

2017 ◽  
Vol 15 (1) ◽  
pp. 1035-1047 ◽  
Author(s):  
Qiaoping Li ◽  
Sanyang Liu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Variable Structure Control ◽  
Variable Structure ◽  
New Method ◽  
Control Technique ◽  
Unknown Parameters ◽  
Structure Control ◽  
Dual Stage

Abstract In this paper, for multiple different chaotic systems with unknown bounded disturbances and fully unknown parameters, a more general synchronization method called modified function projective multi-lag combined synchronization is proposed. This new method covers almost all of the synchronization methods available. As an advantage of the new method, the drive system is a linear combination of multiple chaotic systems, which makes the signal hidden channels more abundant and the signal hidden methods more flexible. Based on the finite-time stability theory and the sliding mode variable structure control technique, a dual-stage adaptive variable structure control scheme is established to realize the finite-time synchronization and to tackle the parameters well. The detailed theoretical derivation and representative numerical simulation is put forward to demonstrate the correctness and effectiveness of the advanced scheme.

scholarly journals Optimal Adaptive Control and Backstepping Control Method with Sliding Mode Differentiator

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Shengxin Sun ◽  
Yang Zhao ◽  
Hao Wu
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Operation Time ◽  
Backstepping Control ◽  
Space Robot ◽  
Robot Arm ◽  
Model Uncertainties ◽  
External Disturbances ◽  
Time Control

In order to improve the success rate of space debris object capture, how to increase the resistance to interference in the space robot arm has become an issue of interest. In addition, since the space operation time is always limited, finite-time control has become another urgent requirement needed to be addressed. Considering external disturbances, two control methods are proposed in this paper to solve the control problem of space robot arm. Firstly, a linear sliding mode control method is proposed considering the model uncertainties and external disturbances. The robot arm can track the desired trajectory, while a trade-off between optimality and robustness of the solved system can be achieved. Then, in order to reduce conservativeness and relax restrictions on external disturbances, a novel backstepping control method based on a finite-time integral sliding mode disturbance observer is developed, which compensates for the effects of both model uncertainties and infinite energy-based disturbance inputs. Finally, simulation examples are given to illustrate the effectiveness of the proposed control method.

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