Chaos synchronization between two different chaotic systems via nonlinear feedback control

This work presents chaos synchronization between two different chaotic systems via nonlinear feedback control. On the basis of a converse Lyapunov theorem and balanced gain scheme, control gains of controller are derived to achieve chaos synchronization for the unified chaotic systems. Numerical simulations are shown to verify the results.     

Synchronization of hyperchaotic systems via linear control

In this paper, synchronization of hyperchaotic system is discussed. Based on the stability theory in the cascade system, a simple linear feedback law is presented to realize synchronization of hyperchaotic systems. Simulation results are given to illustrate the effectiveness of the proposed method.     

Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control

This paper investigates the global synchronization of a class of third-order non-autonomous chaotic systems via the master–slave linear state error feedback control. A sufficient global synchronization criterion of linear matrix inequality (LMI) and several algebraic synchronization criteria for single-variable coupling are proven. These LMI and algebraic synchronization criteria are then applied to two classes of well-known third-order chaotic systems, the generalized Lorenz systems and the gyrostat systems, proving that the local synchronization criteria for the chaotic generalized Lorenz systems developed in the existing literature can actually be extended to describe global synchronization and obtaining some easily implemented synchronization criteria for the gyrostat systems.     

Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach

Based on stability theory of impulsive differential equation and new comparison theory of impulsive differential system, we study the chaos impulsive synchronization of two coupled chaotic systems using the unidirectional linear error feedback scheme. Some generic conditions of chaos impulsive synchronization of two coupled chaotic systems are derived, and to apply the conditions to typical chaotic system––the original Chua’s circuit. The example illustrates the effectiveness of the proposed result.     

Controlling chaotic systems via nonlinear feedback control

In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived.     

Dual synchronization of chaotic systems via time-varying gain proportional feedback

In this paper the dual synchronization of chaotic systems via output feedback strategy is investigated. The slave chaotic systems are fed by a scalar signal generated by a linear combination of the master systems state variables. The sufficient condition and design procedure for dual synchronization are presented. The proposed method is applied for dual synchronization of the Lorenz–Rossler, Rossler–Chen and Duffing–Van der Pol chaotic systems through computer simulation. The results show the effectiveness and feasibility of the proposed algorithm.     

Stabilization and synchronization of chaotic systems via intermittent control

In this paper, we consider the stabilization and synchronization of chaotic systems via intermittent control with time varying control period and control width. Compared to existing results, some less conservative conditions are derived to guarantee the stabilization of nonlinear system. An effective adaptive-intermittent control law is also presented. Two examples are given to verify our proposed results.     

The sufficient criteria for global synchronization of chaotic power systems under linear state-error feedback control

This paper investigates global complete synchronization of two identical power systems and global robust synchronization of two power systems with parameter mismatch and external disturbance, both under the master–slave linear state-error feedback control. Some criteria for achieving the synchronization via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. These algebraic criteria are further optimized so as to improve their performances. The effectiveness of the new algebraic criteria is illustrated by the numerical examples.     

Reduced-order synchronization of uncertain chaotic systems via adaptive control

We consider the coupling of two uncertain dynamical systems with different orders using an adaptive feedback linearization controller to achieve reduced-order synchronization between the two systems. Reduced-order synchronization is the problem of synchronization of a slave system with projection of a master system. The synchronization scheme is an exponential linearizing-like controller and a state/uncertainty estimator. As an illustrative example, we show that the dynamical evolution of a second-order driven oscillator can be synchronized with the canonical projection of a fourth-order chaotic system. Simulation results indicated that the proposed control scheme can significantly improve the synchronousness performance. These promising results justify the usefulness of the proposed output feedback controller in the application of secure communication.     

Global chaos synchronization of new chaotic systems via nonlinear control

Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e^Te. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach.     

Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems

Chaos synchronization, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, chaos synchronization between nonlinear systems has been extensively studied, and many types of synchronization have been announced. This paper introduces another novel type of chaos synchronization – full state hybrid projective synchronization (FSHPS), which includes complete synchronization, anti-synchronization and projective synchronization as its special item. Based on the Lyapunov’s direct method, the general FSHPS scheme is given and illustrated with Lorenz chaotic system and hyperchaotic Chen system as examples. Numerical simulations are used to verify the effectiveness of the proposed scheme.     

Robust sliding-mode backstepping design for synchronization control of cross-strict feedback hyperchaotic systems with unmatched uncertainties

This paper is concerned with the synchronization problem for a class of hyperchaotic chaotic systems. Using sliding mode control approach and backstepping control, a robust control scheme is proposed to make most of the synchronization errors of the systems to zero for matched and unmatched uncertainties. And only one of the synchronization errors of the systems may not be zero, but it is bounded. Meanwhile, the chattering phenomenon is eliminated. The proposed methods can be applied to a variety of chaos systems which can be described by the so-called cross-strict feedback form. Numerical simulations are given to demonstrate the efficiency of the proposed control schemes.     

Phase and anti-phase synchronization of fractional order chaotic systems via active control

This paper is devoted to investigate the phase and anti-phase synchronization between two identical and non-identical fractional order chaotic systems using techniques from active control theory. The techniques are applied to fractional order chaotic Lü and Liu systems. Numerical results demonstrate the effectiveness and feasibility of the proposed control techniques.     

Stabilizing periodic orbits of fractional order chaotic systems via linear feedback theory

In this paper stabilizing unstable periodic orbits (UPO) in a chaotic fractional order system is studied. Firstly, a technique for finding unstable periodic orbits in chaotic fractional order systems is stated. Then by applying this technique to the fractional van der Pol and fractional Duffing systems as two demonstrative examples, their unstable periodic orbits are found. After that, a method is presented for stabilization of the discovered UPOs based on the theories of stability of linear integer order and fractional order systems. Finally, based on the proposed idea a linear feedback controller is applied to the systems and simulations are done for demonstration of controller performance.     

On a new time-delayed feedback control of chaotic systems

In this paper, using the idea of the successive dislocation feedback method, a new time-delayed feedback control method called the successive dislocation time-delayed feedback control (SDTDFC) is designed. Firstly, the idea of SDTDFC is introduced. Then some analytic sufficient conditions of the chaos control from the SDTDFC approach are derived for stabilization. Finally, some established results are further clarified via a case study of the Lorenz system with the numerical simulations.     

Fuzzy delayed output feedback synchronization for time-delayed chaotic systems

In this paper, we propose a new fuzzy delayed output feedback synchronization (FDOFS) method for time-delayed chaotic systems. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the FDOFS controller is designed and an analytic expression of the controller is shown. The proposed controller can guarantee asymptotical synchronization of both drive and response systems. The FDOFS controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed FDOFS method.     

Guaranteed cost control of time-delay chaotic systems via memoryless state feedback

This paper studies the problem of guaranteed cost control for a class of time-delay chaotic systems via memoryless state feedback. A design procedure is proposed to construct a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and achieves an adequate level of performance. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

On synchronization of three chaotic systems

In this paper, a simple but efficient method is applied to the synchronization of three chaotic systems, i.e., the chaotic Lorenz, Chua, and Chen systems. Numerical simulations show this method works very well.     

Achieving synchronization between the fractional-order hyperchaotic Novel and Chen systems via a new nonlinear control technique

In this work, we discuss the stability conditions for a nonlinear fractional-order hyperchaotic system. The fractional-order hyperchaotic Novel and Chen systems are introduced. The existence and uniqueness of solutions for two classes of fractional-order hyperchaotic Novel and Chen systems are investigated. On the basis of the stability conditions for nonlinear fractional-order hyperchaotic systems, we study synchronization between the proposed systems by using a new nonlinear control technique. The states of the fractional-order hyperchaotic Novel system are used to control the states of the fractional-order hyperchaotic Chen system. Numerical simulations are used to show the effectiveness of the proposed synchronization scheme.     

Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control

In this paper, we investigate the synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. Using a combination of Riccati differential equation approach, Lyapunov-Krasovskii functional, inequality techniques, some sufficient conditions for exponentially stability of the error system are formulated in form of a solution to the standard Riccati differential equation. The designed controller ensures that the synchronization of non-autonomous chaotic systems are proposed via delayed feedback control and intermittent linear state delayed feedback control. Numerical simulations are presented to illustrate the effectiveness of these synchronization criteria.