Generalized heterochronous synchronization in coupled time-delayed chaotic systems

A new kind of generalized heterochronous synchronization phenomenon is reported. Different kinds of generalized synchronous states (including generalized anticipated, isochronous and lag projective synchronization) coexist among different state variables between two unidirectionally coupled time-delayed chaotic systems. The analytical conditions for generalized heterochronous synchronization are obtained. We also find that the synchronization conditions are independent of the delay times in the original time-delayed system. The theoretical results are well confirmed by the numerical simulations and electronic circuit experiments.     

Pragmatical adaptive synchronization of different orders chaotic systems with all uncertain parameters via nonlinear control

A new adaptive synchronization scheme by pragmatical asymptotically stability theorem is proposed in this paper. Based on this theorem and nonlinear control theory, a new adaptive synchronization scheme to design controllers can be obtained and especially the constraints for minimum values of feedback gain K in controllers can be derived. This new strategy shows that the constraint values of feedback gain K are related to the error of unknown and estimated parameters if the goal system is given. Through this new strategy, an appropriate feedback gain K can be always decided easily to obtain controllers achieving adaptive synchronization. Two identical Lorenz systems with different initial conditions and two completely different nonlinear systems with different orders, augmented R?ssler??s system and Mathieu?Cvan der Pol system, are used for illustrations to demonstrate the efficiency and effectiveness of the new adaptive scheme in numerical simulation results.     

Review article on adaptive synchronization of chaotic systems with unknown parameters

This review article studies some adaptive chaos synchronization methods that were already presented in the literature for a general class of chaotic systems. In this regard, the proposed adaptive controllers and parameter update laws in several papers are inspected, and it is shown that many works suffer from novelty and they can be categorized in a union set.     

Adaptive finite-time stabilization of uncertain non-autonomous chaotic electromechanical gyrostat systems with unknown parameters

This paper deals with the problem of robust finite-time stabilization of non-autonomous chaotic gyrostat systems. It is assumed that the parameters of the gyrostat system are completely unknown in advance and the system is perturbed by unknown uncertainties and disturbances. Some update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and the update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in a finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to demonstrate the applicability and robustness of the proposed finite-time controller and to verify the theoretical results.     

Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control

In this paper, we apply the nonsingular terminal sliding mode control technique to realize the novel combination-combination synchronization between combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability theory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems. In theory, it is proved that the sliding mode technique can realize fast convergence for four different chaotic systems in the finite time. Some criteria and corollaries are derived for finite-time combination-combination synchronization of four different chaotic systems. Numerical simulation results are shown to verify the effectiveness and correctness of the combination-combination synchronization.     

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.     

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.

     

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.     

Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications

Nonlinear Dynamics - This paper is concerned with the finite-time synchronization problem of coupled drive-response systems with time-varying delays via quantized adaptive aperiodically...     

A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters

A modified adaptive control method is developed in this article and the parameters identification method is then applied in fractional order systems with unknown parameters. The new modified control method based on Lyapunov stability theory is successfully applied to investigate the synchronization of pair of fractional order systems amongst Genesio–Tesi, Qi and Chen systems. By means of the Adams–Bosford–Moulton method, the numerical results show that the modified method is easy to implement and reliable for synchronizing the two different fractional order chaotic systems.     

A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs

In this paper, the problem of finite-time chaos synchronization between two different uncertain chaotic systems with unknown parameters and input nonlinearities is investigated. It is assumed that both master and slave systems are perturbed by unknown model uncertainties, external disturbances, and fully unknown parameters. Proper update laws are proposed to estimate the systems?? unknown parameters. Based on the update laws and finite-time control technique, a robust adaptive controller is introduced to guarantee the convergence of the slave system trajectories to the trajectories of the master system in a given finite time. Two illustrative examples are presented to illustrate the effectiveness and applicability of the proposed finite-time controller and to validate the theoretical results of the paper.     

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.     

Finite-time real combination synchronization of three complex-variable chaotic systems with unknown parameters via sliding mode control

The problem of real combination synchronization between three complex-variable chaotic systems with unknown parameters is investigated by nonsingular terminal sliding mode control in a finite time. Based on the adaptive laws and finite-time stability theory, a nonsingular terminal sliding mode control is designed to ensure the real combination synchronization of three complex-variable chaotic systems in a given finite time. It is theoretically gained that the introduced sliding mode technique has finite-time convergence and stability in both arriving and sliding mode phases. Numerical simulation results are given to show the effectiveness and reliability of the finite-time real combination synchronization.     

Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances

This paper studies the robust adaptive full state hybrid projective synchronization (FSHPS) scheme for a class of chaotic complex systems with uncertain parameters and external disturbances. By introducing a compensator and using nonlinear control and adaptive control, the robust adaptive FSHPS scheme is derived, which can eliminate the influence of uncertainties effectively and achieve adaptive FSHPS of the chaotic (hyperchaotic) complex systems asymptotically with a small error bound. The adaptive laws of the unknown parameters are given, and the sufficient conditions of realizing FSHPS are derived as well. Moreover, we also discuss the case that parameters of chaotic complex system are complex. Finally, the complex Chen system and Lü system, and the hyperchaotic complex Lorenz system are taken as two examples and the numerical simulations are provided to verify the effectiveness and robustness of the proposed control scheme.     

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.     

Finite-time generalized synchronization of chaotic systems with different order

In this paper, the generalized synchronization of chaotic systems with different order is studied. The definition of finite-time generalized synchronization is put forward for the first time. Based on the finite-time stability theory, two control strategies are proposed to realize the generalized synchronization of chaotic systems with different order in finite time. Besides the relation between the parameter β, the initial states of systems and the convergent time were obtained. The corresponding numerical simulations are presented to demonstrate the effectiveness of proposed schemes.     

Complete synchronization of chaotic complex nonlinear systems with uncertain parameters

Our main objective in this work is to investigate complete synchronization (CS) of n-dimensional chaotic complex systems with uncertain parameters. An adaptive control scheme is designed to study the synchronization of chaotic attractors of these systems. We applied this scheme, as an example, to study complete synchronization of chaotic attractors of two identical complex Lorenz systems. The adaptive control functions and the parameters estimation laws are calculated analytically based on the complex Lyapunov function. We show that the error dynamical systems are globally stable. Numerical simulations are computed to check the analytical expressions of adaptive controllers.