scholarly journals Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 122 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Chaotic Oscillator ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Terminal Sliding Mode ◽  
Sliding Mode Controllers ◽  
Empirical Tests ◽  
System States

In this study, the design of an adaptive terminal sliding mode controller for the stabilization of port Hamiltonian chaotic systems with hidden attractors is proposed. This study begins with the design methodology of a chaotic oscillator with a hidden attractor implementing the topological framework for its respective design. With this technique it is possible to design a 2-D chaotic oscillator, which is then converted into port-Hamiltonia to track and analyze these models for the stabilization of the hidden chaotic attractors created by this analysis. Adaptive terminal sliding mode controllers (ATSMC) are built when a Hamiltonian system has a chaotic behavior and a hidden attractor is detected. A Lyapunov approach is used to formulate the adaptive device controller by creating a control law and the adaptive law, which are used online to make the system states stable while at the same time suppressing its chaotic behavior. The empirical tests obtaining the discussion and conclusions of this thesis should verify the theoretical findings.

Robust Synchronization of Fractional-Order Arneodo Chaotic Systems Using a Fractional Sliding Mode Control Strategy

2018 ◽  
pp. 1-22
Author(s):  
Samir Ladaci ◽  
Karima Rabah ◽  
Mohamed Lashab
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Mode Control ◽  
Control Configuration ◽  
The Stability

This chapter investigates a new control design methodology for the synchronization of fractional-order Arneodo chaotic systems using a fractional-order sliding mode control configuration. This class of nonlinear fractional-order systems shows a chaotic behavior for a set of model parameters. The stability analysis of the proposed fractional-order sliding mode control law is performed by means of the Lyapunov stability theory. Simulation examples on fractional-order Arneodo chaotic systems synchronization are provided in presence of disturbances and noises. These results illustrate the effectiveness and robustness of this control design approach.

scholarly journals Design of Terminal Sliding Mode Controllers for Disturbed Non-Linear Systems Described by Matrix Differential Equations of the Second and First Orders

2019 ◽  
Vol 9 (11) ◽  
pp. 2325 ◽  
Author(s):  
Paweł Skruch ◽  
Marek Długosz
Keyword(s):  
Differential Equations ◽  
Sliding Mode ◽  
Sliding Surface ◽  
Terminal Sliding Mode ◽  
Sliding Mode Controllers ◽  
System Trajectory ◽  
Non Linear ◽  
Matrix Differential Equations ◽  
Non Linear Systems ◽  
Matrix Differential

This paper describes a design scheme for terminal sliding mode controllers of certain types of non-linear dynamical systems. Two classes of such systems are considered: the dynamic behavior of the first class of systems is described by non-linear second-order matrix differential equations, and the other class is described by non-linear first-order matrix differential equations. These two classes of non-linear systems are not completely disjointed, and are, therefore, investigated together; however, they are certainly not equivalent. In both cases, the systems experience unknown disturbances which are considered bounded. Sliding surfaces are defined by equations combining the state of the system and the expected trajectory. The control laws are drawn to force the system trajectory from an initial condition to the defined sliding surface in finite time. After reaching the sliding surface, the system trajectory remains on it. The effectiveness of the approaches proposed is verified by a few computer simulation examples.

scholarly journals Robust Adaptive Fractional Fast Terminal Sliding Mode Controller for Microgyroscope

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Juntao Fei ◽  
Zhe Wang ◽  
Xiao Liang
Keyword(s):  
Tracking Control ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Finite Convergence ◽  
Trajectory Tracking Control ◽  
Terminal Sliding Mode ◽  
Fast Terminal Sliding Mode ◽  
Robust Adaptive ◽  
System States ◽  
Terminal Sliding Surface

In this paper, a robust adaptive fractional fast terminal sliding mode controller is introduced into the microgyroscope for accurate trajectory tracking control. A new fast terminal switching manifold is defined to ensure fast finite convergence of the system states, where a fractional-order differentiation term emerges into terminal sliding surface, which additionally generates an extra degree of freedom and leads to better performance. Adaptive algorithm is applied to estimate the damping and stiffness coefficients, angular velocity, and the upper bound of the lumped nonlinearities. Numerical simulations are presented to exhibit the validity of the proposed method, and the comparison with the other two methods illustrates its superiority.

scholarly journals S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium

2019 ◽  
Vol 9 (4) ◽  
pp. 781 ◽  
Author(s):  
Xiong Wang ◽  
Ünal Çavuşoğlu ◽  
Sezgin Kacar ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Encryption Algorithm ◽  
Phase Portraits ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Image Encryption Algorithm

Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented.

Adaptive non-singular terminal sliding mode controller: new design for full control of the quadrotor with external disturbances

2016 ◽  
Vol 39 (3) ◽  
pp. 371-383 ◽  
Author(s):  
Alireza Modirrousta ◽  
Mahdi Khodabandeh
Keyword(s):  
Position Control ◽  
Sliding Mode ◽  
Control Input ◽  
External Disturbances ◽  
Terminal Sliding Mode ◽  
Nonlinear Disturbance Observer ◽  
Tuning Method ◽  
Regular Control ◽  
Control Scheme ◽  
Sliding Mode Controllers

This paper proposes two different adaptive robust sliding mode controllers for attitude, altitude and position control of a quadrotor. Firstly, it proposes a backstepping non-singular terminal sliding mode control with an adaptive algorithm that is applied to the quadrotor for free chattering, finite time convergence and robust aims. In this control scheme instead of regular control input, the derivative of the control input is achieved from a non-singular terminal second-layer sliding surface. An adaptive tuning method is utilized to deal with the external disturbances whose upper bounds are not required to be known in advance in the inner loop. Secondly, a nonlinear disturbance observer based on the integral sliding mode with adaptive gains is proposed for position control, which is known as the outer loop. Stability and robustness of the proposed controller are proved by using the classical Lyapunov criterion. The simulation results demonstrate the validation of the proposed control scheme.

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