Adaptive impulsive synchronization of uncertain drive-response complex-variable chaotic systems

In this paper, impulsive synchronization of drive-response complex-variable chaotic systems is investigated. The drive-response systems with known parameters is considered via impulsive control and adaptive scheme as well as systems with unknown parameters. Noticeably, adaptive strategy is adopted to relax the restriction on the impulsive interval, and the system parameters need not to be known beforehand. According to the Lyapunov stability theory, some synchronization criteria are derived and verified by several numerical simulations.     

Control and synchronization for a class of new chaotic systems via linear feedback

This paper presents a class of new chaotic systems containing two system parameters and a nonlinear term. The complicated dynamics are studied by virtue of theoretical analysis, numerical simulation and spectrum of Lyapunov exponents. Based on Lyapunov stability criteria, the simple sufficient conditions for the design of appropriate linear state feedback controllers to stabilize and synchronize globally the new chaotic systems are presented.     

Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems

In drive-response complex-variable systems, projective synchronization with respect to a real number, real matrix, or even real function means that drive-response systems evolve simultaneously along the same or inverse direction in a complex plane. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, this paper investigates projective synchronization in drive-response networks of coupled complex-variable chaotic systems with respect to complex numbers, called complex projective synchronization (CPS). The adaptive feedback control method is adopted first to achieve CPS in a general drive-response network. For a special class of drive-response networks, the CPS is achieved via pinning control. Furthermore, a universal pinning control scheme is proposed via the adaptive coupling strength method, several simple and useful criteria for CPS are obtained, and all results are illustrated by numerical examples.     

Practical adaptive synchronization of a class of uncertain chaotic systems

This paper studies the practical adaptive synchronization of a class of uncertain chaotic systems in the drive-response framework. An adaptive response system is designed to practically synchronize a given drive chaotic system with uncertainties. An improved adaptation law on the upper bound of uncertainties is proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. The efficiency and effectiveness of the proposed approach is illustrated by computer simulation.     

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.     

Global finite-time synchronization of a class of the non-autonomous chaotic systems

This paper investigates the global finite-time synchronization of a class of the second-order nonautonomous chaotic systems via a master?Cslave coupling. A?continuous generalized linear state-error feedback controller with simple structure is introduced into the synchronization scheme. Some easily implemented algebraic criteria for achieving the global finite-time synchronization are proven and then optimized for the purposes of improving their sharpness. The optimized criteria are applied to a practical master?Cslave synchronization scheme for the single-machine-infinite-bus (SMIB) systems, obtaining the precise corresponding synchronization conditions. Several numerical examples are provided to illustrate the effectiveness of the new synchronization criteria.     

Adaptive synchronization of fractional-order chaotic systems via a single driving variable

This letter investigates the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on sliding mode variable structure control theory and adaptive control technique, a single-state adaptive-feedback controller containing a novel fractional integral sliding surface is developed to synchronize a class of fractional-order chaotic systems. The present controller, which only contains a single driving variable, is simple both in design and implementation. Simulation results for three fractional-order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.     

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.     

Projective synchronization of a class of chaotic systems by dynamic feedback control method

This paper investigates the projective synchronization problem of a class of chaotic systems in arbitrary dimensions. Firstly, a necessary and sufficient condition for the existence of the projective synchronization problem is presented. And this condition is equivalent to check whether a group of algebraic equations about \(\alpha \) have solutions or not. Secondly, an algorithm is proposed to obtain all the solutions of the projective synchronization problem. Thirdly, a simple and physically implementable controller is designed to ensure the realization of the projective synchronization. Finally, three numerical examples are provided to verify the effectiveness and the validity of the proposed results.     

Robust adaptive synchronization for a class of chaotic systems with actuator failures and nonlinear uncertainty

This paper is concerned with the robust adaptive synchronization problem for a class of chaotic systems with actuator failures and unknown nonlinear uncertainty. Combining adaptive method and linear matrix inequality (LMI) technique, a novel type of robust adaptive reliable synchronization controller is proposed, which can eliminate the effect of actuator fault and nonlinear uncertainty on systems. After solving a set of LMIs, synchronization error between the master chaotic and slave chaotic systems can converge asymptotically to zero. Finally, illustrate examples about chaotic Chua’s circuit system and Lorenz systems are provided to demonstrate the effectiveness and applicability of the proposed design method.     

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.     

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.     

Adaptive synchronization of chaotic systems with unknown parameters via new backstepping strategy

In this paper, a new effective approach??backstepping with Ge?CYao?CChen (GYC) partial region stability theory (called BGYC in this article) is proposed to applied to adaptive synchronization. Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller, and it presents a systematic procedure for selecting a proper controller in chaos synchronization. We further combine the systematic backstepping design and GYC partial region stability theory in this article, Lyapunov function can be chosen as a simple linear homogeneous function of states, and the controllers and the update laws of parameters shall be much simpler. Further, it also introduces less simulation error??the numerical simulation results show that the states errors and parametric errors approach to zero much more exactly and efficiently, which are compared with the original one. Two cases are presented in the simulation results to show the effectiveness and feasibility of our new strategy.     

Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach

Backstepping design is proposed for adaptive synchronization of a class of chaotic systems with unknown bounded uncertainties. An adaptive backstepping control law is derived to make the error signals between the master and slave systems asymptotically synchronized without knowing the upper-bounds of the uncertainties in advance. The stability analysis is proved by using a well-known Lyapunov stability. Two illustrative examples are presented to show the effectiveness of the proposed adaptive chaos synchronization.     

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.     

A practical synchronization approach for fractional-order chaotic systems

A practical synchronization approach is proposed for a class of fractional-order chaotic systems to realize perfect \(\delta \)-synchronization, and the nonlinear functions in the fractional-order chaotic systems are all polynomials. The \(\delta \)-synchronization scheme in this paper means that the origin in synchronization error system is stable. The reliability of \(\delta \)-synchronization has been confirmed on a class of fractional-order chaotic systems with detailed theoretical proof and discussion. Furthermore, the \(\delta \)-synchronization scheme for the fractional-order Lorenz chaotic system and the fractional-order Chua circuit is presented to demonstrate the effectiveness of the proposed method.