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.

     

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.     

Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

This paper is concerned with the stabilization problem of uncertain chaotic systems with input nonlinearity. The slope parameters of this nonlinearity are unmeasured. A new sliding function is designed, then an adaptive sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time and finite-time reachability is theoretically proved. Using a virtual state feedback control technique, sufficient condition for the asymptotic stability of sliding mode dynamics is derived via linear matrix inequality (LMI). Then the results can be extended to uncertain chaotic systems with disturbances and adaptive sliding mode H _∞ controllers are designed. Finally, a simulation example is presented to show the validity and advantage of the proposed method.     

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...     

Modified projective synchronization of fractional-order chaotic systems via active sliding mode control

This paper is devoted to study the problem of modified projective synchronization of fractional-order chaotic system. Base on the stability theorems of fractional-order linear system, active sliding mode controller is proposed to synchronize two different fractional-order systems. Moreover, the controller is robust to the bounded noise. Numerical simulations are provided to show the effectiveness of the analytical results.     

Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new fuzzy sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Lü chaotic system and an integer-order Liu chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen??s system and an integer-order hyperchaotic system based upon the Lorenz system, and the synchronization between a fractional-order hyperchaotic system based on Chen??s system, and an integer-order Liu chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.     

Fractional order fixed-time nonsingular terminal sliding mode synchronization and control of fractional order chaotic systems

This paper presents fractional order fixed-time nonsingular terminal sliding mode control for stabilization and synchronization of fractional order chaotic systems with uncertainties and disturbances. First, a novel fractional order terminal sliding mode surface is proposed to guarantee the fixed-time convergence of system states along the sliding surface. Second, a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and remain on it forever. Furthermore, the fractional Lyapunov stability theory is used to prove the fixed-time stability and the robustness of the proposed control scheme and estimate the upper bound of convergence time. Next, the proposed control scheme is applied to the synchronization of two nonidentical fractional order Liu chaotic systems and chaos suppression of fractional order power system. Simulation results verify the effectiveness of the proposed control scheme. Finally, some application issues about the proposed scheme are discussed.

     

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.     

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

In this paper, we apply the nonsingular terminal sliding mode control technique to realize the novel combination-combination synchronization between combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability theory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems. In theory, it is proved that the sliding mode technique can realize fast convergence for four different chaotic systems in the finite time. Some criteria and corollaries are derived for finite-time combination-combination synchronization of four different chaotic systems. Numerical simulation results are shown to verify the effectiveness and correctness of the combination-combination synchronization.     

Terminal sliding mode control for aeroelastic systems

An aeroelastic system is a nonlinear system with two freedoms, i.e., the plunge displacement and the pitch angle, in a dynamic system model. A chaos effect or a limit cycle oscillation is presumably attributed to the nonlinear effect of the pitch angle mentioned above or the interaction between the aerodynamic behaviors. It is that a single trailing edge input in an aeroelastic system is employed as a way to suppress the limit cycle oscillation with an exclusive choice between the plunge displacement and the pitch angle for a control law design. Consequently, the remaining inevitably turns into an internal dynamics, whose stability is adversely affected by the flight speed and structure parameters, a problem improved by no means using a singe control input design. Toward this end, this work presents a controller design criterion with multiple input channels for both the leading and training edges to remove the uncertainty effect of internal dynamics, and render more room for the response design of the plunge displacement as well as the pitch angle. Mostly due to external disturbance and unknown uncertainty, there is a deviation between the intended and implemented system performances for a robust control design, a mainstream research issue in the modern control. As a consequence of a sliding mode control utilized here, the limit cycle oscillation suffered in an aeroelastic system is removed effectively by the use of a terminal sliding mode control, and the chattering phenomenon seen in the control signal is hence eliminated by his method. It is seen from simulations that the control system is stably assured to reach the target within a limited time frame with an addition of a saturation function to the control law.     

Control of a class of fractional-order chaotic systems via sliding mode

This paper investigates the chaos control of a class of fractional-order chaotic systems via sliding mode. First, the sliding mode control law is derived to make the states of the fractional-order chaotic systems asymptotically stable. Second, the designed control scheme guarantees asymptotical stability of the uncertain fractional-order chaotic systems in the presence of an external disturbance. Finally, simulation results are given to demonstrate the effectiveness of the proposed sliding mode control method.     

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

In this paper, we use sliding mode control integrated with an interval type-2 fuzzy system for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the Sliding Mode Control (SMC), an interval fuzzy type-2 logic controller is used. In addition, an adaptive interval type-2 fuzzy inference approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic system. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy approximators. The stability analysis for the proposed control scheme is provided, and simulation results compare the performance of interval type-2 fuzzy and type-1 fuzzy controllers to verify the effectiveness of the proposed method.     

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.     

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

The problem of real combination synchronization between three complex-variable chaotic systems with unknown parameters is investigated by nonsingular terminal sliding mode control in a finite time. Based on the adaptive laws and finite-time stability theory, a nonsingular terminal sliding mode control is designed to ensure the real combination synchronization of three complex-variable chaotic systems in a given finite time. It is theoretically gained that the introduced sliding mode technique has finite-time convergence and stability in both arriving and sliding mode phases. Numerical simulation results are given to show the effectiveness and reliability of the finite-time real combination synchronization.     

On the sliding mode control of mechanical systems

We consider the control of mechanical systems based on sliding mode control techniques. Recently developed simplex control methods are shown to converge in a finite time when applied to nonlinear systems under bounded deterministic uncertainty. Applications are considered to the control of mechanical systems in which the control action is provided by monodirectional devices.     

Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme

This paper brings attention to the chaotic antisynchronization and synchronization for a novel class of chaotic systems with different structure and dimensions by using a new sliding mode control strategy. This approach needs only n?1 controllers, where n is the number of the salve system dimensions. And our method uses proportional integral (PI) surface and saturation function to simplify the task of assigning the performance of the closed-loop error system in sliding motion. Furthermore, the sufficient conditions are derived, and representative examples are proposed as well. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the proposed control scheme, which are in agreement with theoretical analysis.     

On dynamic sliding mode control of nonlinear fractional-order systems using sliding observer

Nonlinear Dynamics - In this study, a new fractional-order dynamic sliding mode control (FDSMC) for a class of nonlinear systems is presented. In FDSMC, an integrator is placed before the input...