Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.     

Robust synchronization of uncertain fractional-order chaotic systems with time-varying delay

This paper presents a new technique using a recurrent non-singleton type-2 sequential fuzzy neural network (RNT2SFNN) for synchronization of the fractional-order chaotic systems with time-varying delay and uncertain dynamics. The consequent parameters of the proposed RNT2SFNN are learned based on the Lyapunov–Krasovskii stability analysis. The proposed control method is used to synchronize two non-identical and identical fractional-order chaotic systems, with time-varying delay. Also, to demonstrate the performance of the proposed control method, in the other practical applications, the proposed controller is applied to synchronize the master–slave bilateral teleoperation problem with time-varying delay. Simulation results show that the proposed control scenario results in good performance in the presence of external disturbance, unknown functions in the dynamics of the system and also time-varying delay in the control signal and the dynamics of system. Finally, the effectiveness of proposed RNT2SFNN is verified by a nonlinear identification problem and its performance is compared with other well-known neural networks.     

Disturbance-observer-based robust synchronization control of uncertain chaotic systems

In this paper, a robust synchronization control scheme is proposed for chaotic systems in the presence of system uncertainties and unknown external disturbances. For the synchronization error system, the compound disturbance which is estimated using the disturbance observer cannot be directly measured. If the gain matrix is properly chosen, the disturbance observer can approximate the unknown compound disturbance well. And then, the constrained robust synchronization control scheme is presented for uncertain chaotic systems based on the output of disturbance observer. In the design of a robust synchronization control scheme, the effect of unknown control input constraint has been explicitly considered to guarantee the synchronization performance. Numerical simulation results are presented to illustrate the effectiveness of the proposed constrained synchronization control scheme for uncertain chaotic systems.     

Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer

This paper proposes a robust adaptive backstepping synchronization method for a class of uncertain chaotic systems. Unknown factors including system uncertainties and external disturbances are estimated by a fuzzy disturbance observer. By use of the fuzzy disturbance observer, any prior information about the unknown factors is not need. The proposed method using the estimated values guarantees the global synchronization for chaotic systems with mismatched uncertainties in the sense of uniform ultimate boundedness. Finally, numerical examples are presented to show the effectiveness of the method.     

Synchronization of chaotic systems using fuzzy impulsive control

This paper investigates the problem of fuzzy impulsive control to synchronize two chaotic systems using a novel time-dependent Lyapunov function approach. Compared with the existing time-independent Lyapunov methods, the proposed method enables us to exploit more information on the impulsive intervals. Initially, using the Lyapunov technique and two parameterized linear matrix inequality (LMI) techniques, some less conservative synchronization criteria via a fuzzy impulsive controller using the states of both drive and response chaotic systems are derived. Subsequently, an LMI approach to designing such a fuzzy impulsive controller is developed to realize the synchronization. Finally, the proposed method is applied to the chaotic Lorenz system and Rösler system to illustrate its effectiveness.     

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.     

Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization

In this study, we investigate a class of chaotic synchronization and anti-synchronization with stochastic parameters. A controller is composed of a compensation controller and a fuzzy controller which is designed based on fractional stability theory. Three typical examples, including the synchronization between an integer-order Chen system and a fractional-order Lü system, the anti-synchronization of different 4D fractional-order hyperchaotic systems with non-identical orders, and the synchronization between a 3D integer-order chaotic system and a 4D fractional-order hyperchaos system, are presented to illustrate the effectiveness of the controller. The numerical simulation results and theoretical analysis both demonstrate the effectiveness of the proposed approach. Overall, this study presents new insights concerning the concepts of synchronization and anti-synchronization, synchronization and control, the relationship of fractional and integer order nonlinear systems.     

Lag synchronization for fuzzy chaotic system based on fuzzy observer

A new fuzzy observer for lag synchronization is given in this paper. By investi- gating synchronization of chaotic systems, the structure of drive-response lag synchronization for fuzzy chaos system based on fuzzy observer is proposed. A new lag synchronization criterion is derived using the Lyapunov stability theorem, in which control gains are obtained under the LMI condition. The proposed approach is applied to the well-known Chen＇s systems. A simulation example is presented to illustrate its effectiveness.     

Adaptive synchronization for uncertain complex dynamical network using fuzzy disturbance observer

This paper proposes a robust adaptive controller design method for synchronization of a complex dynamical network with uncertainty and disturbance. A fuzzy disturbance observer is used to estimate the overall disturbances without any prior knowledge about them. The proposed control method globally asymptotically synchronizes the network using adaptation laws obtained by using Lyapunov stability theory. The proposed method is applied to two chaotic systems and the results show the effectiveness of the approach.     

Adaptive fuzzy synchronization for a class of chaotic systems with unknown nonlinearities and disturbances

By incorporating a time-varying parameter into T-S fuzzy logic systems with nonlinear consequents (T-S-FLS-NRC), the synchronization of driver-response chaotic systems with unknown nonlinearities and disturbances is synthesized via state feedback controllers and updated adaptive laws. During designing process of synchronization, only three common parameters are needed to be adjusted automatically, and the number of adaptive laws is not related with the number of IF-THEN rules. Meanwhile, T-S-FLS-NRC is employed to approximate the unknown nonlinearities for the master and slave systems. The general form and high approximate capacity of T-S-FLS-NRC is useful to obtain fewer fuzzy rules than other fuzzy logic systems such as Mamdani or T-S fuzzy logic system with linear consequents. The synchronization method in this paper cannot only significantly reduce the on-line computational burden, but also can synthesize the fuzzy rules with high interpretability by means of intuition inferences. Finally, a numerical example is used to show the validity of the proposed synchronization method.     

A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems

In this paper, a projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive controller is investigated for a projective synchronization of uncertain multivariable chaotic systems. The adaptive fuzzy-logic systems are used to approximate the unknown functions. A decomposition property of the control gain matrix is used in the controller design and the stability analysis. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the synchronization errors to an adjustable region. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.     

Intelligent quadratic optimal synchronization of?uncertain chaotic systems via LMI approach

This paper proposes an intelligent quadratic optimal control scheme via linear matrix inequality (LMI) approach for the synchronization of uncertain chaotic systems with both external disturbances and parametric perturbations. First, a four-layered neural fuzzy network (NFN) identifier is constructed to estimate system nonlinear dynamics. Based on the NFN identifier, an intelligent quadratic optimal controller is developed with robust hybrid control scheme, in which H _?? optimal control and variable structure control (VSC) are embedded to attenuate the effects of external disturbances and parametric perturbations. The adaptive tuning laws of network parameters are derived in the sense of the Lyapunov synthesis approach to ensure network convergence, and the sufficient criterion for existence of the controller is formulated in the linear matrix inequality (LMI) form to guarantee the quadratic optimal synchronization performance. Finally, a numerical simulation example is illustrated by the chaotic Chua??s circuit system to demonstrate the effectiveness of our scheme.     

Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties

This paper solves the problem of robust synchronization of nonlinear chaotic gyrostat systems in a given finite time. The parameters of both master and slave chaotic gyrostat systems are assumed to be unknown in advance. In addition, the gyrostat systems are disturbed by unknown model uncertainties and external disturbances. Suitable update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in finite time. The precise value of the convergence time is given. A numerical simulation demonstrates the applicability and efficiency of the proposed finite-time synchronization strategy.     

Robust chaos synchronization of fractional-order chaotic systems with unknown parameters and uncertain perturbations

Chaotic systems in practice are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems. Based on Lyapunov stability theory and a fractional-order differential inequality, a modified adaptive control scheme and adaptive laws of parameters are developed to robustly synchronize coupled fractional-order chaotic systems with unknown parameters and uncertain perturbations. This synchronization approach is simple, global and theoretically rigorous. Simulation results for two fractional-order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.     

Synchronization of unified chaotic system by sliding mode/mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

This paper deals with the synchronization of uncertain unified chaotic system in the presence of two kinds of disturbances, white noise and bounded power signal. A sliding mode controller (SMC) is established to guarantee the sliding motion. Moreover, a proportional-integral (PI) switching surface is used to determine the performance of the system in the sliding motion. Also, by using a mixed H ₂/H _∞ approach, the effect of external disturbances on the sliding motion is reduced. The necessary parameters of constructing controller and switching surface are found via semidefinite programming (SDP) which can be solved effectively by a standard software. Finally, a numerical simulation is presented to show the effectiveness of the proposed method.     

Design of fractional robust adaptive intelligent controller for uncertain fractional-order chaotic systems based on active control technique

In this paper, a robust fractional-order adaptive intelligent controller is proposed for stabilization of uncertain fractional-order chaotic systems. The intelligent neuro-fuzzy network is used to estimate unknown dynamics of system, while the neuro-fuzzy network parameters as well as the upper bounds of the model uncertainties, disturbances and approximation errors are adaptively estimated via separate adaptive rules. An SMC scheme, with a fractional-order sliding surface, is employed, as the controller to improve the velocity and performance of the proposed control system and to eliminate the unknown but bounded uncertainties, external disturbances and approximation errors. The Lyapunov stability theorem has been also employed to show the stability of the closed-loop system, robustness against uncertainties, external disturbances and approximation errors, while the control signal remains bounded. Explanatory examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.     

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.

     

Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach

In this paper, an adaptive sliding mode control method is introduced to ensure robust synchronization of two different fractional-order chaotic systems with fully unknown parameters and external disturbances. For this purpose, a fractional integral sliding surface is defined and an adaptive sliding mode controller is designed. In this method, no knowledge of the bounds of parameters and perturbation is required in advance and the parameters are updated through an adaptive control process. The proposed scheme is global and theoretically rigorous. Two examples are given to illustrate effectiveness of the scheme, in which the synchronizations between fractional-order chaotic Chen system and fractional-order chaotic Rössler system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.

     

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.

     

A new chaotic attractor and its robust function projective synchronization

We introduce a simple chaotic system that contains one multiplier and one quadratic term. The system is similar to the generalized Lorenz system but is not topologically equivalent. The properties of the proposed chaotic system are examined by theoretical and numerical analysis. An analog chaotic circuit is implemented that realizes the chaotic system for the verification of its attractor. Furthermore, we propose a robust function projective synchronization using time delay estimation. A numerical simulation of synchronization between the proposed system and the Lorenz system demonstrates that the proposed approach provides fast and robust synchronization even in the presence of unknown parameter variations and disturbances.