Chameleon Chaotic Systems with Quadratic Nonlinearities: An Adaptive Finite-Time Sliding Mode Control Approach and Circuit Simulation

In this chapter a new direct adaptive fuzzy optimal sliding mode control approach is proposed for the stabilization of fractional chaotic systems with different initial conditions of the state under the presence of uncertainties and external disturbances. Using Lyapunov analysis, the direct adaptive fuzzy optimal sliding mode control approach illustrates asymptotic convergence of error to zero as well as good robustness against external disturbances and uncertainties. The authors present a method for optimum tuning of sliding mode control system parameter using particle swarm optimization (PSO) algorithm. PSO is a robust stochastic optimization technique based on the movement and intelligence of swarm, applying the concept of social interaction to problem solving. Simulation examples for the control of nonlinear fractional-order systems are given to illustrate the effectiveness of the proposed fractional adaptive fuzzy control strategy.

Synchronization of Lorenz System Based on Fast Stabilization Sliding Mode Control

Mathematical Problems in Engineering ◽

10.1155/2015/282919 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Xu Guowei ◽

Wan Zhenkai ◽

Li Chunqing

Keyword(s):

Sliding Mode Control ◽

Finite Time ◽

Lorenz System ◽

Sliding Mode ◽

External Perturbation ◽

Lyapunov Theory ◽

Continuous Control ◽

Integral Sliding Mode ◽

Control Approach ◽

Mode Control

A sliding mode control approach is achieved for Lorenz system based on optimal finite time convergent and integral sliding mode surface. The system perturbation is divided into two parts: the unmatched and the matched parts. Firstly, we design a discontinuous control for the unmatched part which will not be amplified. Secondly, we design a continuous control, that is, the ideal control to stabilize the Lorenz system error states in finite time stabilization. Then the controller based on integral sliding mode is constructed to ensure the robustness. The proposed method is proven to guarantee the stability and the robustness using the Lyapunov theory in the system uncertainties and external perturbation. Finally, the numerical simulations demonstrate that the proposed controller is effective and robust with respect to the perturbation.

Finite-time real combination synchronization of three complex-variable chaotic systems with unknown parameters via sliding mode control

Nonlinear Dynamics ◽

10.1007/s11071-017-3338-z ◽

2017 ◽

Vol 88 (3) ◽

pp. 1677-1690 ◽

Cited By ~ 76

Author(s):

Junwei Sun ◽

Yuanyuan Wu ◽

Guangzhao Cui ◽

Yanfeng Wang

Keyword(s):

Sliding Mode Control ◽

Complex Variable ◽

Finite Time ◽

Chaotic Systems ◽

Sliding Mode ◽

Unknown Parameters ◽

Combination Synchronization ◽

Mode Control

Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control

Nonlinear Dynamics ◽

10.1007/s11071-013-1133-z ◽

2013 ◽

Vol 76 (1) ◽

pp. 383-397 ◽

Cited By ~ 64

Author(s):

Junwei Sun ◽

Yi Shen ◽

Xiaoping Wang ◽

Jie Chen

Keyword(s):

Sliding Mode Control ◽

Finite Time ◽

Chaotic Systems ◽

Sliding Mode ◽

Unknown Parameters ◽

Combination Synchronization ◽

Mode Control ◽

Different Chaotic Systems

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

Frontiers in Applied Mathematics and Statistics ◽

10.3389/fams.2021.589406 ◽

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.

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Journal of Control Science and Engineering ◽

10.1155/2017/9562818 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 5

Author(s):

Xiaona Song ◽

Shuai Song ◽

Ines Tejado Balsera ◽

Leipo Liu ◽

Lei Zhang

Keyword(s):

Sliding Mode Control ◽

Fractional Order ◽

Finite Time ◽

Chaotic Systems ◽

Sliding Mode ◽

Sliding Surface ◽

Fuzzy Sliding Mode Control ◽

Mode Control ◽

Fuzzy Sliding Mode ◽

Terminal Sliding Surface

The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.

Finite-time coordination in multiagent systems using sliding mode control approach

Automatica ◽

10.1016/j.automatica.2014.02.019 ◽

2014 ◽

Vol 50 (4) ◽

pp. 1209-1216 ◽

Cited By ~ 60

Author(s):

Masood Ghasemi ◽

Sergey G. Nersesov

Keyword(s):

Sliding Mode Control ◽

Multiagent Systems ◽

Finite Time ◽

Sliding Mode ◽

Control Approach ◽

Mode Control

A continuous integral terminal sliding mode control approach for a class of uncertain nonlinear systems

Measurement and Control ◽

10.1177/0020294019836113 ◽

2019 ◽

Vol 52 (5-6) ◽

pp. 720-728

Author(s):

Huawei Niu ◽

Qixun Lan ◽

Yamei Liu ◽

Huafeng Xu

Keyword(s):

Nonlinear Systems ◽

Sliding Mode Control ◽

Finite Time ◽

Sliding Mode ◽

Control Law ◽

Terminal Sliding Mode Control ◽

Terminal Sliding Mode ◽

Control Approach ◽

Mode Control ◽

Time Control

In this article, the continuous integral terminal sliding mode control problem for a class of uncertain nonlinear systems is investigated. First of all, based on homogeneous system theory, a global finite-time control law with simple structure is proposed for a chain of integrators. Then, inspired by the proposed finite-time control law, a novel integral terminal sliding mode surface is designed, based on which an integral terminal sliding mode control law is constructed for a class of higher order nonlinear systems subject disturbances. Furthermore, a finite-time disturbance observer-based integral terminal sliding mode control law is proposed, and strict theoretical analysis shows that the composite integral terminal sliding mode control approach can eliminate chattering completely without losing disturbance attenuation ability and performance robustness of integral terminal sliding mode control. Simulation examples are given to illustrate the simplicity of the new design approach and effectiveness.