scholarly journals Estimation of Synchronization Errors between Master and Slave Chaotic Systems with Matched/Mismatched Disturbances and Input Uncertainty

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 176
Author(s):  
Chih-Hsueh Lin ◽  
Guo-Hsin Hu ◽  
Jun-Juh Yan
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Control Input ◽  
Input Uncertainty ◽  
Input Nonlinearity ◽  
Synchronization Errors ◽  
Riemann Sum ◽  
Sliding Manifold ◽  
Error Dynamics ◽  
Mismatched Disturbances

This study is concerned with robust synchronization for master–slave chaotic systems with matched/mismatched disturbances and uncertainty in the control input. A robust sliding mode control (SMC) is presented to achieve chaos synchronization even under the influence of matched/mismatched disturbances and uncertainty of inputs. A proportional-integral (PI) switching surface is introduced to make the controlled error dynamics in the sliding manifold easy to analyze. Furthermore, by using the proposed SMC scheme even subjected to input uncertainty, we can force the trajectories of the error dynamics to enter the sliding manifold and fully synchronize the master–slave systems in spite of matched uncertainties and input nonlinearity. As for the mismatched disturbances, the bounds of synchronization errors can be well estimated by introducing the limit of the Riemann sum, which is not well addressed in previous works. Simulation experiments including matched and mismatched cases are presented to illustrate the robustness and synchronization performance with the proposed SMC synchronization controller.

Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Derivative ◽  
Sliding Mode ◽  
Variable Structure ◽  
Stability And Convergence ◽  
Control Input ◽  
Fractional Systems ◽  
Sliding Motion ◽  
Efficient Performance ◽  
Sliding Manifold ◽  
Chattering Free

The problem of stabilization of nonlinear fractional systems in spite of system uncertainties is investigated in this paper. First, a proper fractional derivative type sliding manifold with desired stability and convergence properties is designed. Then, the fractional stability theory is adopted to derive a robust sliding control law to force the system trajectories to attain the proposed sliding manifold and remain on it evermore. The existence of the sliding motion is mathematically proven. Furthermore, the sign function in the control input, which is responsible to the being of harmful chattering, is transferred into the fractional derivative of the control input. Therefore, the resulted control input becomes smooth and free of the chattering. Some numerical simulations are presented to illustrate the efficient performance of the proposed chattering-free fractional variable structure controller.

Robust Control for Uncertain Unified Chaotic Systems with Input Nonlinearity via Improved Sliding Mode Technique

2011 ◽  
Vol 474-476 ◽  
pp. 2100-2105
Author(s):  
Xiao Jing Wu ◽  
Xue Li Wu
Keyword(s):  
Robust Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Chen System ◽  
Input Nonlinearity ◽  
Adaptive Parameter ◽  
Unified Chaotic Systems ◽  
Mode Technique ◽  
Sliding Mode Technique

This paper investigates the robust control problem of the uncertain unified chaotic systems subject to sector input nonlinearity. First, the adaptive parameter is introduced for designing sliding surface such that the parameters of the unified chaotic system are not necessary to know. Then, based on Lyapunov theory, the controller is designed via sliding mode technique, which cancels the assumption that the information on the bound of input nonlinearity should be known for designer in advance. Finally, the sliding mode controller is applied to ensure that different uncertain chaotic systems (Lorenz system, Lü system and Chen system) states can be regulated to zero levels asymptotically in the presence of sector input nonlinearity. The simulation results demonstrated the effectiveness of the proposed controller.

Sliding mode control for uncertain unified chaotic systems with input nonlinearity

2007 ◽  
Vol 34 (2) ◽  
pp. 437-442 ◽  
Author(s):  
Tsung-Ying Chiang ◽  
Meei-Ling Hung ◽  
Jun-Juh Yan ◽  
Yi-Sung Yang ◽  
Jen-Fuh Chang
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Input Nonlinearity ◽  
Mode Control ◽  
Unified Chaotic Systems

Chatter alleviation for a class of second-order under-actuated mechanical systems with matched and mismatched disturbances

2016 ◽  
Vol 23 (3) ◽  
pp. 458-468
Author(s):  
Jinjin Shi ◽  
Jinxiang Wang ◽  
Fangfa Fu
Keyword(s):  
Sliding Mode ◽  
Mechanical Systems ◽  
Design Procedure ◽  
Second Order ◽  
Control Input ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Sliding Surfaces ◽  
Low Pass ◽  
Mismatched Disturbances

The chattering phenomenon and a system with both matched and mismatched disturbances are the major difficulties in sliding mode control design. This paper presents an effective design procedure to alleviate these two difficulties for a class of second-order under-actuated mechanical systems. In the proposed design, new hierarchical sliding surfaces are designed and a modified disturbance observer is utilized to estimate the lumped disturbance which is a linear combination of the matched and mismatched disturbances. The chatter in control input is filtered out by an integrator, which acts as a low-pass filter. The asymptotic stabilities of the entire sliding surfaces are guaranteed. A design study considering lateral control of a vehicle with matched and mismatched disturbances demonstrates the effectiveness of the proposed design.

scholarly journals Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

2017 ◽  
Vol 71 (1-2) ◽  
pp. 69-77
Author(s):  
Naeimadeen Noghredani ◽  
Saeed Balochian
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Financial Systems ◽  
External Disturbances ◽  
Sliding Mode Controllers ◽  
Error Dynamic ◽  
Error Dynamics ◽  
Integral Sliding Surface ◽  
The Stability

Abstract Fractional-order chaotic unified systems include a variety of fractional-order chaotic systems such as Chen, Lorenz, Lu, Liu, and financial systems. This paper describes a sliding mode controller for synchronisation of fractional-order chaotic unified systems in the presence of uncertainties and external disturbances, and affirms the stability of the controller (which is composed of error dynamics). Moreover, the synchronisation of two separate fractional-order chaotic systems is studied. For this aim, fractional integral sliding surface is defined. Then the sliding mode control rule for stability of error dynamic is presented based on the Lyapunov stability theorem. Simulation results, obtained by using MATLAB, show that the proposed sliding mode has employed an appropriate approach against uncertainties and to reduce the chattering phenomenon that often occurs with sliding mode controllers.

scholarly journals Integrated Guidance and Control Method for the Interception of Maneuvering Hypersonic Vehicle Based on High Order Sliding Mode Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Kang Chen ◽  
Bin Fu ◽  
Yuening Ding ◽  
Jie Yan
Keyword(s):  
Fourth Order ◽  
Control Method ◽  
Sliding Mode ◽  
High Order ◽  
Control Input ◽  
Guidance And Control ◽  
Near Space ◽  
Sliding Manifold ◽  
Integrated Guidance And Control ◽  
And Control

This paper focuses on the integrated guidance and control (IGC) method applied in the interception of maneuvering near space hypersonic vehicles using the homogeneous high order sliding mode (HOSM) approach. The IGC model is derived by combining the target-missile relative motion and dynamic equations. Then, a fourth-order sliding mode controller is implemented in the augmented IGC model. To estimate the high order derivatives of the sliding manifold which is required in the HOSM method, an Arbitrary Order Robust Exact Differentiator is presented. At last, the idea of virtual control is introduced to alleviate the chattering of the control input without using any saturation functions which may lead to a loss of the robustness. And the stability of the closed-loop system with presented fourth-order homogeneous HOSM controller is also proved theoretically. Finally, simulation results are provided and analyzed to demonstrate the effectiveness of the proposed method in three typical engagement scenarios.

SLIDING MODE CONTROL OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

2000 ◽  
Vol 10 (05) ◽  
pp. 1139-1147 ◽  
Author(s):  
HER-TERNG YAU ◽  
CHA'O-KUANG CHEN ◽  
CHIEH-LI CHEN
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Control Law ◽  
Control Input ◽  
Continuous Control ◽  
Sliding Surfaces ◽  
Design Scheme ◽  
Mode Design ◽  
Uncertain Chaotic Systems

A sliding mode hyperplane design for a class of chaotic systems with uncertainties is considered in this paper. The concept of extended systems is used such that continuous control input is obtained using a sliding mode design scheme. It is guaranteed that under the proposed control law, uncertain chaotic systems can asymptotically track target orbits. The converging speed of error states can be arbitrarily set by assigning the corresponding dynamics to the sliding surfaces. Illustrative examples of a controlled uncertain Duffing–Holmes system are presented.

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