Synchronization in reduced-order of chaotic systems via control approaches based on high-order sliding-mode observer

The reduced-order synchronization problem of two chaotic systems (master–slave) with different dimension and relative degree is considered. A control scheme based on a high-order sliding-mode observer-identifier and a feedback state controller is proposed, where the trajectories of slave can be synchronized with a canonical projection of the master. Thus, the reduced-order synchronization is achieved in spite of master/slave mismatches. Simulation results are provided in order to illustrate the performance of the proposed synchronization scheme.     

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.     

Synchronization of chaotic neural networks with mixed time delays

In this paper, we investigate the synchronization problems of chaotic neural networks with mixed time delays. We first establish the sufficient conditions for synchronization of identical chaotic neural networks with mixed time delays via linear output feedback control. To overcome the difficulty that complete synchronization between nonidentical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of nonidentical chaotic neural networks with mixed time delays, where the parameters and functions are mismatched. Numerical simulations are carried out to illustrate the main results.     

Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays

This paper considers the chaotic synchronization problem of neural networks with time-varying and distributed delays using impulsive control method. By utilizing the stability theory for impulsive functional differential equations, several impulsive control laws are derived to guarantee the exponential synchronization of neural networks with time-varying and distributed delays. It is shown that chaotic synchronization of the networks is heavily dependent on the designed impulsive controllers. Moreover, these conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. Finally, a numerical example and its simulation are given to show the effectiveness and advantage of the proposed control schemes.     

Synchronization of chaotic solid-state Nd:YAG lasers: Application to secure communication

In this paper, the synchronization problem of coupled chaotic lasers in master–slave configuration is numerically studied. The approach used allows to give a simple design procedure for the slave laser. In particular, we consider a complex system composed by two chaotic Nd:YAG lasers coupled through the first state variable of the master laser. Synchronization of chaotic Nd:YAG lasers is achieved by injecting the chaotic signal from the master Nd:YAG laser into the slave Nd:YAG laser. The robustness of synchronization is discussed when a mismatch of parameters occurs, and the effects of the channel noise on recovered information are showed. A potential application of chaotic synchronization of Nd:YAG lasers to transmit encrypted digital information is also given.     

Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators

In this paper, we consider the problem of synchronizing a master–slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master–slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master–slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master–slave chaotic system based on Chua’s circuit.     

Model reference adaptive synchronization of T–S fuzzy discrete chaotic systems using output tracking control

This paper presents a model reference adaptive control approach for the synchronization of a discrete-time chaotic systems using output tracking control. The reference model system is chosen using the output of master system and Takagi–Sugeno (T–S) fuzzy model is employed to represent the discrete-time chaotic slave system. Design the control input so that the controlled slave system achieves asymptotic synchronization with the reference system given that two systems start from different initial conditions, different parameters and/or different type of model. Using a gradient algorithm, the ideal controller gains which can stabilize the error equation are estimated. Simulation examples of two cases are given to demonstrate the validity of our proposed adaptive method.     

Impulsive synchronization of discrete-time chaotic systems under communication constraints

This paper investigates the problem of impulsive synchronization of discrete-time chaotic systems subject to limited communication capacity. Control laws with impulses are derived by using measurement feedback, where the effect of quantization errors is considered. Sufficient conditions for asymptotic stability of synchronization error systems are given in terms of linear matrix inequalities and algebraic inequalities. Some numerical simulations are given to demonstrate the effectiveness of the method.     

Exponential H∞ synchronization for discrete‐time chaotic neural networks with time delays and stochastic perturbations via output feedback control

This paper investigates the problem of exponential H_∞ synchronization of discrete‐time chaotic neural networks with time delays and stochastic perturbations. First, by using the Lyapunov‐Krasovskii (Lyapunov) functional and output feedback controller, we establish the H_∞ performance of exponential synchronization in the mean square of master‐slave systems, which is analyzed using a matrix inequality approach. Second, the parameters of a desired output feedback controller can be achieved by solving a linear matrix inequality. Finally, 2 simulated examples are presented to show the effectiveness of the theoretical results.     

Synchronization and anti-synchronization of chaotic oscillators under input saturation

This paper addresses the design of simple state feedback controllers for synchronization and anti-synchronization of chaotic oscillators under input saturation and disturbance. By employing sector condition, linear matrix inequality (LMI)-based sufficient conditions are derived to design (global or local) controllers for chaos synchronization. The proposed local synchronization strategy guarantees a region of stability in terms of difference between states of the master–slave systems. This region of stability can be enlarged by means of an LMI-based optimization algorithm, through which asymptotic synchronization of chaotic oscillators can be ensured for a large difference in their initial conditions. Further, a novel LMI-based robust control strategy is developed, for local synchronization of input-constrained chaotic oscillators, by providing an upper bound on synchronization error in terms of disturbance and initial conditions of chaotic systems. Moreover, the proposed robust state feedback control methodology is modified to provide an inaugural treatment for robust anti-synchronization of chaotic systems under input saturation and disturbance. The results of the proposed methodologies are verified through numerical simulations for synchronization and anti-synchronization of the master–slave chaotic Chua’s circuits under input saturation.     

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.     

Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control

-In this paper, we investigate the synchronization problems of chaotic fuzzy cellular neural networks with time-varying delays. To overcome the difficulty that complete synchronization between non-identical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of non-identical chaotic fuzzy cellular neural networks with time-varying delays, where the parameters and activation functions are mismatched. This research demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

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.     

Synchronization of the unified chaotic system

This paper studies the synchronization problem of the unified chaotic system. Three different methods, linear feedback method, nonlinear feedback method and impulsive control method are used to control synchronization of the unified chaotic systems. Based on the Lyapunov stability theory and impulsive control method, the conditions of synchronization are discussed, and they are also proved theoretically. Numerical simulations show the effectiveness of the three different methods.     

Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.     

Robust synchronization of delayed neural networks based on adaptive control and parameters identification

This paper investigates synchronization dynamics of delayed neural networks with all the parameters unknown. By combining the adaptive control and linear feedback with the updated law, some simple yet generic criteria for determining the robust synchronization based on the parameters identification of uncertain chaotic delayed neural networks are derived by using the invariance principle of functional differential equations. It is shown that the approaches developed here further extend the ideas and techniques presented in recent literature, and they are also simple to implement in practice. Furthermore, the theoretical results are applied to a typical chaotic delayed Hopfied neural networks, and numerical simulation also demonstrate the effectiveness and feasibility of the proposed technique.     

Master–slave synchronization criteria for chaotic hindmarsh–rose neurons using linear feedback control

This article is concerned with master–slave synchronization for two chaotic Hindmarsh–Rose neurons. The main contribution of this article is that three synchronization criteria are derived by using linear feedback control without the estimation of bounds of state variables of controlled slave neurons. Three simulation examples are used to illustrate the effectiveness of our results. © 2015 Wiley Periodicals, Inc. Complexity 21: 319–327, 2016     

Impulsive control and synchronization of chaotic Hindmarsh–Rose models for neuronal activity

The issues of impulsive control and synchronization of chaotic Hindmarsh–Rose model are investigated in this paper. Based on impulsive control theory of dynamical systems, some simple yet less conservative criteria ensuring impulsive stabilization and synchronization of the Hindmarsh–Rose models are derived analytically. Furthermore, two numerical results are presented to demonstrate the effectiveness of the proposed control techniques. It is shown that the obtained results should be helpful to understand dynamical mechanism of signal encoding and transduction from information processing of real neuronal activity.     

Dynamic Robust Output Min–Max Control for Discrete Uncertain Systems

Min–max control is a robust control, which guarantees stability in the presence of matched uncertainties. The basic min–max control is a static state feedback law. Recently, the applicability conditions of discrete static min–max control through the output have been derived. In this paper, the results for output static min–max control are further extended to a class of output dynamic min–max controllers, and a general parametrization of all such controllers is derived. The dynamic output min–max control is shown to exist in many circumstances under which the output static min–max control does not exist, and usually allows for broader bounds on uncertainties. Another family of robust output min–max controllers, constructed from an asymptotic observer which is insensitive to uncertainties and a state min–max control, is derived. The latter is shown to be a particular case of the dynamic min–max control when the nominal system has no zeros at the origin. In the case where the insensitive observer exists, it is shown that the observer-controller has the same stability properties as those of the full state feedback min–max control.     

Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion

Separate studies have been published on the stability of fuzzy cellular neural networks with time delay in the leakage term and synchronization issue of coupled chaotic neural networks with stochastic perturbation and reaction-diffusion effects. However, there have not been studies that integrate the two fields. Motivated by the achievements from both fields, this paper considers the exponential synchronization problem of coupled chaotic fuzzy cellular neural networks with stochastic noise perturbation, time delay in the leakage term and reaction-diffusion effects using linear feedback control. Lyapunov stability theory combining with stochastic analysis approaches are employed to derive sufficient criteria ensuring the coupled chaotic fuzzy neural networks to be exponentially synchronized. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.