Finite-time synchronization of uncertain unified chaotic systems based on CLF

This paper studies the problem of finite-time synchronization for the unified chaotic systems. We prove that global finite-time synchronization can be achieved for unified chaotic systems which have uncertain parameters. Simulation results for Lorenz, Lü and Chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme.     

Global finite-time synchronization of different dimensional chaotic systems

This paper addresses the problem of global finite-time synchronization of two different dimensional chaotic systems. Firstly, the definition of global finite-time synchronization of different dimensional chaotic systems are introduced. Based on the finite-time stability methods, the controller is designed such that the chaotic systems are globally synchronized in a finite time. Then, some uncertain parameters are adopted in the chaotic systems, new control law and dynamical parameter estimation are proposed to guarantee that the global finite-time synchronization can be obtained. By considering a dynamical parameter designed in the controller, the adaptive updated controller is also designed to achieve the desired results. At last, the results of two different dimensional chaotic systems are also extended to two different dimensional networked chaotic systems. Finally, three numerical examples are given to verify the validity of the proposed methods.     

Identify fully uncertain parameters and design controllers based on synchronization

For a chaotic system with specified structure, all unknown model parameters can be simultaneously identified by a simple combination of adaptive scheme and linear feedback. Furthermore, based on the Lyapunov stability theory, a sufficient condition for chaos synchronization is derived analytically, which guarantees that the system with fully uncertain parameters and the controlled system achieve chaos synchronization. Numerical simulations are presented for demonstration.     

Identify fully uncertain parameters and design controllers based on synchronization

For a chaotic system with specified structure, all unknown model parameters can be simultaneously identified by a simple combination of adaptive scheme and linear feedback. Furthermore, based on the Lyapunov stability theory, a sufficient condition for chaos synchronization is derived analytically, which guarantees that the system with fully uncertain parameters and the controlled system achieve chaos synchronization. Numerical simulations are presented for demonstration.     

Synchronization of mechanical horizontal platform systems in finite time

The horizontal platform system (HPS) is a mechanical device that exhibits rich and chaotic dynamics. In this paper, the problem of finite-time synchronization of two non-autonomous chaotic HPSs is investigated. It is assumed that both drive and response systems are disturbed by model uncertainties, external disturbances and fully unknown parameters. Appropriate update laws are proposed to undertake the unknown parameters. Using the update laws and finite-time control theory, a robust adaptive controller is derived to synchronize the two uncertain HPSs in a given finite time. Subsequently, the effects of input nonlinearities are taken into account and a robust adaptive controller is introduced to synchronize the two uncertain HPSs within a finite time. The finite-time stability and convergence of the proposed schemes are analytically proved. Two illustrative examples are presented to show the robustness and applicability of the proposed adaptive finite-time control techniques.     

Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters

This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of adaptive synchronization between two nearly identical chaotic and hyper-chaotic systems with uncertain parameters is studied. Based on Lyapunov stability theory, a novel adaptive synchronization controller is designed, and the analytic expression of the controller and the adaptive laws of parameters are developed. The controller is simple and systemic, no parameters of the slave system are included in the controller, and, for some specific error systems, the controller can be simplified ulteriorly. New chaotic and a new hyper-chaotic systems with uncertain parameters are taken as the examples to show the effectiveness of the proposed adaptive synchronization method.     

随机扰动下统一混沌系统的有限时间同步

本文研究了具有随机扰动的统一混沌系统的有限时间同步问题,其中随机扰动是一维标准的维纳随机过程.利用了有限时间随机李雅普诺夫稳定性理论、伊藤公式,本文分三个步骤设立了三个控制器获得了驱动–响应系统在有限时间内的均方渐近同步.最后进行的数值模拟验证了理论结果的正确性和方法的有效性.     

Synchronization of Genesio chaotic system via backstepping approach

Backstepping design is proposed for synchronization of Genesio chaotic system. Firstly, the control problem for the chaos synchronization of nominal Genesio systems without unknown parameters is considered. Next, an adaptive backstepping control law is derived to make the error signals between drive Genesio system and response Genesio system with an uncertain parameter asymptotically synchronized. Finally, the approach is extended to the synchronization problem for the system with three unknown parameters. The stability analysis in this article is proved by using a well-known Lyapunov stability theorem. Note that the approach provided here needs only a single controller to realize the synchronization. Two numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.     

Synchronization of unified chaotic systems with uncertain parameters based on the CLF

Chaos synchronization in unified chaotic systems with uncertain parameters is discussed in this paper. On the basis of the control Lyapunov function (CLF), a feedback controller is designed which is only related to the boundaries of the uncertain parameters. Synchronization of two identical unified chaotic systems with different initial conditions is realized. Simulation results for Lorenz, Lü and Chen chaotic systems are provided to verify the effectiveness of the proposed scheme.     

The function cascade synchronization method and applications

In this paper, a new function cascade synchronization method of chaos system is proposed to achieve generalized projective synchronization for chaotic systems. Based on Laypunov stability, the proposed synchronization technique is applied to three famous chaotic systems: the unified chaotic system, Liu system and Rössler system, which can make the states of two identical chaotic systems asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are presented to show the effectiveness.     

Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique

In this paper, the problem of finite-time chaos synchronization between two different chaotic systems with fully unknown parameters is investigated. First, a new nonsingular terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is proved. Then, appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Afterwards, based on the adaptive laws and finite-time control idea, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, some numerical simulations are presented to demonstrate the applicability and effectiveness of the proposed technique.     

Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity

This paper addresses chaos anti-synchronization of uncertain unified chaotic systems with dead-zone input nonlinearity. Using the sliding mode control technique and Lyapunov stability theory, a proportional–integral (PI) switching surface is proposed to ensure the stability of the closed-loop error system in sliding mode. Then a sliding mode controller (SMC) is proposed to guarantee the hitting of the switching surface even with uncertainties and the control input containing dead-zone nonlinearity. Some simulation results are included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.     

Finite-time structure identification and synchronization of drive-response systems with uncertain parameter

This paper proposes an approach of finite-time synchronization to identify the topological structure and unknown parameters simultaneously for under general complex dynamical networks. Based on the finite-time stability theory, an effective control input and a feedback control with an updated law are designed to realize finite-time synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously. Since finite-time topology identification means the suboptimum in identified time, the results of this paper are important. Several useful criteria for finite-time synchronization are given. Finally, two examples simulations for supporting the theoretical results are also provided.     

Adaptive generalized function projective lag synchronization of different chaotic systems with fully uncertain parameters

In this paper, a novel projective synchronization scheme called adaptive generalized function projective lag synchronization (AGFPLS) is proposed. In the AGFPLS method, the states of two different chaotic systems with fully uncertain parameters are asymptotically lag synchronized up to a desired scaling function matrix. By means of the Lyapunov stability theory, an adaptive controller with corresponding parameter update rule is designed for achieving AGFPLS between two diverse chaotic systems and estimating the unknown parameters. This technique is employed to realize AGFPLS between uncertain Lü chaotic system and uncertain Liu chaotic system, and between Chen hyperchaotic system and Lorenz hyperchaotic system with fully uncertain parameters, respectively. Furthermore, AGFPLS between two different uncertain chaotic systems can still be achieved effectively with the existence of noise perturbation. The corresponding numerical simulations are performed to demonstrate the validity and robustness of the presented synchronization method.     

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 two hyperchaotic systems via adaptive control

This letter presents chaos synchronization problem of two different hyperchaotic systems when the parameters of drive and response systems are fully unknown or uncertain. Based on Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are derived such that two different high dimensional chaotic systems are to be synchronized. Hyperchaotic Chen system and Second-harmonic generation (SHG) system are taken as an illustrative example to show the effectiveness of the proposed method.     

Chaos and chaos synchronization for a non-autonomous rotational machine systems

Chaos and chaos synchronization of the centrifugal flywheel governor system are studied in this paper. By mechanics analyzing, the dynamical equation of the centrifugal flywheel governor system is established. Because of the non-linear terms of the system, the system exhibits both regular and chaotic motions. The characteristic of chaotic attractors of the system is presented by the phase portraits and power spectra. The evolution from Hopf bifurcation to chaos is shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lyapunov exponent spectra. This letter addresses control for the chaos synchronization of feedback control laws in two coupled non-autonomous chaotic systems with three different coupling terms, which is demonstrated and verified by Lyapunov exponent spectra and phase portraits. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.     

Global synchronization criterion and adaptive synchronization for new chaotic system

This paper proposes two schemes of synchronization of two four-scorll chaotic attractor, a simple global synchronization and adaptive synchronization in the presence of unknown system parameters. Based on Lyapunov stability theory and matrix measure, a simple generic criterion is derived for global synchronization of four-scorll chaotic attractor system with a unidirectional linear error feedback coupling. This methods are applicable to a large class of chaotic systems where only a few algebraic inequalities are involved. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization method.     

Designing synchronization schemes for chaotic fractional-order unified systems

Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration.     

Adaptive synchronization of uncertain chaotic systems via backstepping design

In this paper, an approach for adaptive synchronization of uncertain chaotic systems is proposed using adaptive backstepping with tuning functions. Strong properties of global stability and asymptotic synchronization can be achieved. The proposed approach offers a systematic design procedure for adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approach.