Adaptive terminal sliding mode control for anti-synchronization of uncertain chaotic systems

This paper presents an adaptive terminal sliding mode control method for anti-synchronization of uncertain chaotic systems. By fusion of the terminal sliding mode control and the adaptive control techniques, a robust controller is designed so that the states tracking error can reach the terminal sliding mode surface and converge to zero in a finite time. Finally, some simulation results are included to demonstrate the effectiveness and the feasibility of the proposed anti-synchronization scheme.     

Robust synchronization of two different uncertain fractional-order chaotic systems via adaptive sliding mode control

This paper proposes a novel robust fractional-order sliding mode approach for the synchronization of two fractional-order chaotic systems in the presence of system parameter uncertain and external disturbance. An adaptive sliding mode controller is constructed resorted to the designed fractional integral type sliding surface. Based on the Lyapunov stability theorem, the stability of the closed error system is proved. Finally, a numerical simulation is performed to illustrate the effectiveness of the proposed method.     

Decentralized sliding mode quantized feedback control for a class of uncertain large-scale systems with dead-zone input

This paper is concerned with the robust quantized feedback stabilization problem for a class of uncertain nonlinear large-scale systems with dead-zone nonlinearity in actuator devices. It is assumed that state signals of each subsystem are quantized and the quantized state signals are transmitted over a digital channel to the controller side. Combined with a proposed discrete on-line adjustment policy of quantization parameters, a decentralized sliding mode quantized feedback control scheme is developed to tackle parameter uncertainties and dead-zone input nonlinearity simultaneously, and ensure that the system trajectory of each subsystem converges to the corresponding desired sliding manifold. Finally, an example is given to verify the validity of the theoretical result.     

Synchronization between uncertain chaotic systems with a diverse structure based on a second-order sliding mode control

Synchronization between uncertain chaotic systems with a diverse structure is investigated using a second-order sliding mode control. Sliding surface, adaptive laws of the unknown parameters, and the sliding mode controller are designed based on stability theory. The Van der Pol system with chaotic behavior in physics is taken as a target system; the Duffing system with unknown parameters is taken as a response system. The artificial simulation results show that this method is still effective.     

Forced sliding mode control for chaotic systems synchronization

Synchronization of chaotic systems is considered to be a common engineering problem. However, the proposed laws of synchronization control do not always provide robustness toward the parametric perturbations. The purpose of this article is to show the use of synergy-cybernetic approach for the construction of robust law for Arneodo chaotic systems synchronization. As the main method of design of robust control, the method of design of control with forced sliding mode of the synergetic control theory is considered. To illustrate the effectiveness of the proposed law, in this article it is compared with the classical sliding mode control and adaptive backstepping. The distinctive features of suggested robust control law are the more good compensation of parametric perturbations (better performance indexes—the root-mean-square error (RMSE), average absolute value (AVG) of error) without designing perturbation observers, the ability to exclude the chattering effect, less energy consuming and a simpler analysis of the stability of a closed-loop system. The study of the proposed control law and the change of its parameters and the place of parametric perturbation’s application is carried out. It is possible to significantly reduce the synchronization error and RMSE, as well as AVG of error by reducing some parameters, but that leads to an increase in control signal amplitude. The place of application of parametric disturbances (slave or master system) has no effect on the RMSE and AVG of error. Offered approach will allow a new consideration for the design of robust control laws for chaotic systems, taking into account the ideas of directed self-organization and robust control. It can be used for synchronization other chaotic systems.

     

Neural adaptive control of uncertain chaotic systems with input and output saturation

Nonlinear Dynamics - This paper is concerned with the neural adaptive control design problem of a class of chaotic systems with uncertain dynamics, input and output saturation. To attenuate the...     

Observer-based model reference adaptive control for unknown time-delay chaotic systems with input nonlinearity

Existence of unknown time-delay in the systems is a drastic restriction that it can menace the stability criteria and even deteriorate the performance system. This undesired case would be more intensified if that the uncertain input nonlinearity effects are also considered. To handle the input nonlinearities effects (results in dead-zone and/or hysteresis phenomena) and also unknown time-delay in the chaotic systems, this paper presents an observer-based Model Reference Adaptive Control (MRAC) scheme for a class of unknown time-delay chaotic systems with disturbances. This new method is a delay-independent variable-structure control method which is integrated with an observer system. The main task of the proposed approach is to accomplish a perfect tracking procedure such that unknown parameters are adapted via output estimation error. Furthermore, stability of the closed-loop system is achieved by means of the Lyapunov stability theory. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.     

Global sliding mode control and application in chaotic systems

This paper is concerned with the stabilization problem for a class of nonlinear systems. Using the global sliding mode control approach, a novel robust control law is established to make the state of system stable and to improve the robustness and the stability of system. A new reaching law is introduced to reduce the chattering. Finally, the method is applied to chaotic systems and an example of the chaotic system is given to illustrate the advantage of the proposed method.     

Sliding mode control with adaptive fuzzy dead-zone compensation for uncertain chaotic systems

The dead-zone nonlinearity is frequently encountered in many industrial automation equipments and its presence can severely compromise control system performance. In this work, an adaptive variable structure controller is proposed to deal with a class of uncertain nonlinear systems subject to an unknown dead-zone input. The adopted approach is primarily based on the sliding mode control methodology but enhanced by an adaptive fuzzy algorithm to compensate the dead-zone. Using Lyapunov stability theory and Barbalat??s lemma, the convergence properties of the closed-loop system are analytically proven. In order to illustrate the controller design methodology, an application of the proposed scheme to a chaotic pendulum is introduced. A comparison between the stabilization of general orbits and unstable periodic orbits embedded in chaotic attractor is carried out showing that the chaos control can confer flexibility to the system by changing the response with low power consumption.     

Adaptive robust fuzzy control for a class of uncertain chaotic systems

In this paper, the output feedback control of uncertain chaotic systems is addressed via an adaptive robust fuzzy approach. Fuzzy logic systems are employed to approximate uncertain nonlinear functions in the chaotic systems. Because only partial information of the system’s states is needed to be known, an observer is given to estimate the unmeasured states. Compared with the existing results in the observer design, the prior knowledge on dynamic uncertainties is relaxed and a class of more general chaotic systems is considered as well as robustness to the approximation error is improved. It can be proven that the closed-loop system is stable in the sense that all the variables are bounded. Simulation example for the unified chaotic systems is given to verify the effectiveness of the proposed method. This work was supported in part by the National Natural Science Foundation of China (60874056) and the Foundation of Educational Department of Liaoning Province (2008312).     

Adaptive sliding mode control of a chaotic nonsmooth-air-gap permanent magnet synchronous motor with uncertainties

Using the sliding mode control approach, a simple adaptive controller design method is proposed for a chaotic nonsmooth-air-gap permanent magnet synchronous motor (PMSM). The proposed method does not require the restrictive assumption that accurate information on the PMSM parameter and load torque values is available, thus it has robustness to model uncertainties. This paper analyzes the stability and convergence of the closed-loop control system, and this paper gives a discretized control algorithm for DSP implementation. Finally, this paper presents some simulation results to illuminate that the proposed method can effectively handle the controller design problem for a chaotic nonsmooth-air-gap PMSM under inaccurate information on the PMSM parameter and load torque values.     

Chattering reduced sliding mode control for a class of chaotic systems

Nonlinear Dynamics - This paper presents a sliding mode control scheme for chaotic systems. Finite time stability of the system states is realized by implementing the proposed controller, which is...     

Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach

Nonlinear Dynamics - This paper seeks to address the problem of finite-time stabilization for a class of uncertain Hamiltonian systems via sliding mode control approach. A novel sliding function in...     

Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input

In this paper, we present an adaptive control scheme for a class of uncertain nonlinear system with unknown nonsymmetric dead-zone nonlinearity. It is assumed that the system states are unmeasurable. Therefore, an observer is designed to estimate those unmeasured states. The controller is designed by using the backstepping control design procedure. The proposed adaptive scheme requires only the information that the dead-zone slopes are bounded. The new control scheme ensures bounded-error trajectory tracking and the boundedness of all the signals in the closed-loop. The feasibility is investigated by an illustrative simulation example.     

Adaptive terminal sliding mode control for nonlinear differential inclusion systems with disturbance

This paper deals with the adaptive terminal sliding mode control for nonlinear differential inclusion systems subjected to disturbance. The upper bound of the disturbance is unknown. First, the fast terminal sliding mode surface is established and sufficient condition for fast convergence is given. Then the adaptive sliding mode controller is designed to make the state of system arrive at the sliding mode in finite time. A numerical example is provided to show the effectiveness of the proposed method.