Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

Adaptive synchronization of uncertain Liu system via nonlinear input

This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.

Adaptive synchronization of a critical chaotic system

This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters.Theoretical analysis and numerical simulations showthe effectiveness and feasibility of the proposed schemes.

Adaptive coupled synchronization of non-autonomous systems in ring networks

The adaptive coupled synchronization method for non-autonomous systems is proposed. This method can avoid estimating the value of coupling coefficient. Under the uniform Lipschitz assumption, we derive the asymptotical synchronization for a general coupling ring network with N identical non-autonomous systems~ even when N is large enough. Strict theoretical proofs are given. Numerical simulations illustrate the effectiveness of the present method.

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.

Adaptive synchronization in an array of asymmetric coupled neural networks

This paper investigates the global synchronization in an array of linearly coupled neural networks with constant and delayed coupling. By a simple combination of adaptive control and linear feedback with the updated laws, some sufficient conditions are derived for global synchronization of the coupled neural networks. The coupling configuration matrix is assumed to be asymmetric, which is more coincident with the realistic network. It is shown that the approaches developed here extend and improve the earlier works. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Breaking chaotic shift key communication via adaptive key identification

This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter mismatch is used for chaos adaptive synchronization and parameter identification. An index function about the synchronization error is defined and conjugate gradient method is used to minimize the index function and to search the transmitter＇s parameter （key）. By using proposed method, secure key is recovered from transmitted signal generated by low dimensional chaos and hyper chaos switching communication. Multi-parameters can also be identified from the transmitted signal with noise.

Robust adaptive synchronization of chaotic neural networks by slide technique

In this paper, we focus on the robust adaptive synchronization between two coupled chaotic neural networks with all the parameters unknown and time-varying delay. In order to increase the robustness of the two coupled neural networks, the key idea is that a sliding-mode-type controller is employed. Moreover, without the estimate values of the network unknown parameters taken as an updating object, a new updating object is introduced in the constructing of controller. Using the proposed controller, without any requirements for the boundedness, monotonicity and differentiability of activation functions, and symmetry of connections, the two coupled chaotic neural networks can achieve global robust synchronization no matter what their initial states are. Finally, the numerical simulation validates the effectiveness and feasibility of the proposed technique.

Adaptive synchronization of uncertain chaotic systems via switching mechanism

This paper deals with the problem of synchronization for a class of uncertain chaotic systems. The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error, with unknown growth rate. A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on the Lyapunov approach, the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities. To demonstrate the efficiency of the proposed scheme, the well-known chaotic system namely Chua＇s circuit is considered as an illustrative example.

Encoding-decoding message for secure communication based on adaptive chaos synchronization

In this paper, based on an adaptive chaos synchronization scheme, two methods of encoding-decoding message for secure communication are proposed. With the first method, message is directly added to the chaotic signal with parameter uncertainty. In the second method, multi-parameter modulation is used to simultaneously transmit more than one digital message （i.e., the multichannel digital communication） through just a single signal, which switches among various chaotic attractors that differ only subtly. In theory, such a treatment increases the difficulty for the intruder to directly intercept the information, and meanwhile the implementation cost decreases significantly. In addition, numerical results show the methods are robust against weak noise, which implies their practicability.

Synchronization of hyperchaotic Chen systems:a class of the adaptive control approach

The synchronization of hyperchaotic Chen systems is considered. An adaptive synchronization approach and a cascade adaptive synchronization approach are presented to synchronize a drive system and a response system. By utilizing an adaptive controller based on the dynamic compensation mechanism, exact knowledge of the systems is not necessarily required, and the synchronous speed is controllable by tuning the controller parameters. Sufficient conditions for the asymptotic stability of the two synchronization schemes are derived. Numerical simulation results demonstrate that the adaptive synchronization scheme with four control inputs and the cascade adaptive synchronization scheme with only one control signal are effective and feasible in chaos synchronization of hyperchaotic systems.

Adaptive Synchronization of Rssler System Based on Dynamic Surface Control

A synchronization scheme for R6ssler system based on Dynamic Surface Control （DSC） is proposed in this paper. The DSC method is a recursive design procedure like conventional backstepping methods. Different from the backstepping design, a first-order fdter is introduced in every DSC design step. For this introduced fdter, the derivative of the selected virtual control is avoided and then the drawback of ＂explosion of complexity＂ existing in backstepping design is overcome. Moreover, adaptive method is used for controller design when the system parameters are unknown. Finally, a numerical example is given to illustrate the effectiveness and performance of the proposed method.

Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lya-punov＇s stability theory, linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an Hoe-norm constraint. Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.

Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay

This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.

Outer synchronization of uncertain small-world networks via adaptive sliding mode control

The outer synchronization of irregular coupled complex networks is inves- tigated with nonidentical topological structures. The switching gain is estimated by an adaptive technique, and a sliding mode controller is designed to satisfy the sliding con- dition. The outer synchronization between two irregular coupled complex networks with different initial conditions is implemented via the designed controllers with the corre- sponding parameter update laws. The chaos synchronization of two small-world networks consisting of N uncertain identical Lorenz systems is achieved to demonstrate the appli- cations of the proposed approach.

Adaptive synchronization of different kinds of chaotic neural networks

The purpose of the paper is to present an adaptive control method for the synchronization of different classes of chaotic neural networks. A new sufficient condition for the global synchronization of two kinds of chaotic neural networks is derived. The proposed control method is efficient for implementing the synchronization when the parameters of the drive system are different from those of the response system. A numerical example is used to demonstrate the validity of the proposed method and the obtained result.

Adaptive H_∞ Synchronization of Master-slave Systems with Mixed Time-varying Delays and Nonlinear Perturbations: An LMI Approach

This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaptation law including the master-slave parame- ters are established for designing a delayed synchronization law in terms of linear matrix inequalities（LMIs）. The time-varying controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. Particularly, it is shown that the synchronization speed can be controlled by adjusting the updated gain of the synchronization signal. Two numerical examples are given to demonstrate the effectiveness of the method.

Adaptive synchronization of chaotic systems with less measurement and actuation

We investigate the synchronization problem between identical chaotic systems only when necessary measurement(output)and actuation(input)are needed to be implemented by the adaptive controllers.A sufficient condition is derived based on the Lyapunov stability theory and Schur complementary lemma.Moreover,the theoretic result is applied to the Rikitake system and the hyperchaotic Liu system to show its effectiveness and correctness.Numerical simulations are presented to verify the results.

Adaptive Synchronization in Small-World Dynamical Networks

Adaptive synchronization in NW small-world dynamical networks was studied. Firstly, an adaptive synchronization method is presented and explained. Then, it is applied to two different classes of dynamical networks, one is a class-B network, small-world connected R6 ssler oscillators, the other is a class-A network, small-world connected Chua＇s circuits. The simulation verifies the validity of the presented method. It also shows that the adaptive synchronization method is robust to the variations of the node systems parameters. So the presented method can be used in networks whose node systems have unknown or time-varying parameters.

Adaptive lag synchronization and parameter identification of fractional order chaotic systems

This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic L/i system is used to illustrate the validity of this theoretic method.