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.

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.

Immersion and invariance adaptive finite-time control of air-breathing hypersonic vehicles

2018 ◽  
Vol 233 (7) ◽  
pp. 2626-2641 ◽  
Author(s):  
Chao Han ◽  
Zhen Liu ◽  
Jianqiang Yi
Keyword(s):  
Control System ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Second Order ◽  
Hypersonic Vehicles ◽  
Terminal Sliding Mode ◽  
Air Breathing ◽  
Immersion And Invariance ◽  
Time Control

In this paper, a novel adaptive finite-time control of air-breathing hypersonic vehicles is proposed. Based on the immersion and invariance theory, an adaptive finite-time control method for general second-order systems is first derived, using nonsingular terminal sliding mode scheme. Then the method is applied to the control system design of a flexible air-breathing vehicle model, whose dynamics can be decoupled into first-order and second-order subsystems by time-scale separation principle. The main features of this hypersonic vehicle control system lie in the design flexibility of the parameter adaptive laws and the rapid convergence to the equilibrium point. Finally, simulations are conducted, which demonstrate that the control system has the features of fast and accurate tracking to command trajectories and strong robustness to parametric and non-parametric uncertainties.

A New Finite Time Control Solution for Robotic Manipulators Based on Nonsingular Fast Terminal Sliding Variables and the Adaptive Super-Twisting Scheme

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Vo Anh Tuan ◽  
Hee-Jun Kang
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Robotic Manipulators ◽  
Control Law ◽  
Continuous Control ◽  
Terminal Sliding Mode ◽  
Finite Time Convergence ◽  
Position Errors ◽  
Time Control

In this study, a new finite time control method is suggested for robotic manipulators based on nonsingular fast terminal sliding variables and the adaptive super-twisting method. First, to avoid the singularity drawback and achieve the finite time convergence of positional errors with a fast transient response rate, nonsingular fast terminal sliding variables are constructed in the position errors' state space. Next, adaptive tuning laws based on the super-twisting scheme are presented for the switching control law of terminal sliding mode control (TSMC) so that a continuous control law is extended to reject the effects of chattering behavior. Finally, a new finite time control method ensures that sliding motion will take place, regardless of the effects of the perturbations and uncertainties on the robot system. Accordingly, the stabilization and robustness of the suggested control system can be guaranteed with high-precision performance. The robustness issue and the finite time convergence of the suggested system are totally confirmed by the Lyapunov stability principle. In simulation studies, the experimental results exhibit the effectiveness and viability of our proposed scheme for joint position tracking control of a 3DOF PUMA560 robot.

Fixed-time fractional-order sliding mode control for nonlinear power systems

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1425-1434 ◽  
Author(s):  
Sunhua Huang ◽  
Jie Wang
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Fixed Time ◽  
Sliding Mode Controller ◽  
Mode Control ◽  
Time Control

In this study, a fractional-order sliding mode controller is effectively proposed to stabilize a nonlinear power system in a fixed time. State trajectories of a nonlinear power system show nonlinear behaviors on the angle and frequency of the generator, phase angle, and magnitude of the load voltage, which would seriously affect the safe and stable operation of the power grid. Therefore, fractional calculus is applied to design a fractional-order sliding mode controller which can effectively suppress the inherent chattering phenomenon in sliding mode control to make the nonlinear power system converge to the equilibrium point in a fixed time based on the fixed-time stability theory. Compared with the finite-time control method, the convergence time of the proposed fixed-time fractional-order sliding mode controller is not dependent on the initial conditions and can be exactly evaluated, thus overcoming the shortcomings of the finite-time control method. Finally, superior performances of the fractional-order sliding mode controller are effectively verified by comparing with the existing finite-time control methods and integral order sliding mode control through numerical simulations.

scholarly journals Finite-Time Synchronization for Uncertain Master-Slave Chaotic System via Adaptive Super Twisting Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
P. Siricharuanun ◽  
C. Pukdeboon
Keyword(s):  
Sliding Mode Control ◽  
Chaotic System ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Second Order ◽  
Control Technique ◽  
Mode Control ◽  
Twisting Algorithm ◽  
Second Order Sliding Mode

A second-order sliding mode control for chaotic synchronization with bounded disturbance is studied. A robust finite-time controller is designed based on super twisting algorithm which is a popular second-order sliding mode control technique. The proposed controller is designed by combining an adaptive law with super twisting algorithm. New results based on adaptive super twisting control for the synchronization of identical Qi three-dimensional four-wing chaotic system are presented. The finite-time convergence of synchronization is ensured by using Lyapunov stability theory. The simulations results show the usefulness of the developed control method.

scholarly journals Finite-Time Synchronization Between Two Different Chaotic Systems by Adaptive Sliding Mode Control

2021 ◽  
Vol 7 ◽  
Author(s):  
Nipaporn Tino ◽  
Piyapong Niamsup
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Sliding Mode Control ◽  
Terminal Sliding Mode ◽  
Mode Control ◽  
Different Chaotic Systems

The finite-time chaos synchronization between two different chaotic systems with uncertain parameters and external disturbances is studied. A new and improved adaptive fast nonsingular terminal sliding mode control (ANFTSM) has been designed for a fast rate convergence of tracking error to zero in finite time. The effectiveness of the proposed control method is shown in simulation results.

scholarly journals Adaptive chattering-free terminal sliding-mode control for full-order nonlinear system with unknown disturbances and model uncertainties

2020 ◽  
Vol 17 (3) ◽  
pp. 172988142092529
Author(s):  
Lei Wan ◽  
Guofang Chen ◽  
Mingwei Sheng ◽  
Yinghao Zhang ◽  
Ziyang Zhang
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Upper Bound ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Control Law ◽  
Sliding Mode Controller ◽  
Terminal Sliding Mode ◽  
Chattering Free

This study investigates an adaptive chattering-free sliding-mode control method for n-order nonlinear systems with unknown external disturbances and uncertain models. The proposed method takes the advantage of finite-time fast convergence to avoid singularity problem and ensure its robustness against system uncertainty and unknown disturbance. To achieve fast convergence from any initial condition to system origin, a full-order terminal sliding-mode controller containing differential terms is proposed based on the property of n-order nonlinear systems. Then the continuous and smooth actual control law is obtained by integrating the differential control law containing the discontinuous sign function to realize chattering free. Meanwhile, instead of evaluating the fixed upper bound of system uncertainty and interference in practical implementations, an adaptive method is utilized for its unknown upper bound estimation. The convergence of the adaptive terminal sliding-mode controller in finite time is verified based on Lyapunov stability theory. Finally, two simulation results demonstrate the effectiveness of the proposed control method.

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