Adaptive control of chaotic systems based on a single layer neural network

This Letter presents an adaptive neural network control method for the chaos control problem. Based on a single layer neural network, the dynamic about the unstable fixed period point of the chaotic system can be adaptively identified without detailed information about the chaotic system. And the controlled chaotic system can be stabilized on the unstable fixed period orbit. Simulation results of Henon map and Lorenz system verify the effectiveness of the proposed control method.     

Adaptive synchronisation of fractional-order chaotic systems

A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.     

Survival probability and saturation energy in periodically driven quantum chaotic systems

We study characteristics of the steady state of a random-matrix model with periodical pumping, where the energy increase saturates by quantum localization. We study the dynamics by making use of the survival probability. We found that Floquet eigenstates are separated into the localized and extended states, and the former governs the dynamics.     

Adaptive impulsive synchronization of uncertain chaotic systems

The Letter develops an adaptive impulsive scheme that includes a sole restriction criterion to achieve synchronization of chaotic nonlinear systems with unknown parameters. The system is assumed to satisfy the local Lipschitz condition while a Lipschitz constant and the uncertain system parameters are estimated by augmented adaptation equations. Adaptation of all parameters is proven to converge exponentially. The significance of the related control parameters and their margins in the criterion is also discussed in detail. The Lorenz system has been simulated to illustrate the theoretical analysis.     

Exponential stabilization of chaotic systems with delay by periodically intermittent control

This paper studies the exponential stabilization problem for a class of chaotic systems with delay by means of periodically intermittent control. A unified exponential stability criterion, together with its simplified versions, is established by using Lyapunov function and differential inequality techniques. A suboptimal intermittent controller is designed with respect to the general cost function under the assumption that the control period is fixed. Numerical simulations on two chaotic oscillators are presented to verify the theoretical results.     

Adaptive synchronization of Rossler and Chen chaotic systems

A novel adaptive synchronization method is proposed for two identical Rossler and Chen systems with uncertain parameters. Based on Lyapunov stability theory, we derive an adaptive controller without the knowledge of the system parameters, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized. Especially, when some unknown uncertain parameters are positive, we can make the controller more simple and, besides, the controller is independent of those positive uncertain parameters. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.     

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.     

Correlations in the adiabatic response of chaotic systems

Adiabatic variation of the parameters of a chaotic system results in a fluctuating reaction force. The quantum analog of a classical dissipative force, proportional to the time integral of the force-force correlation function, vanishes. We study this quantum-classical crossover for random matrix models. For the Gaussian unitary ensemble the crossover is found to take place on the Heisenberg time scale and the finite time integral practically vanishes for longer times. For the Gaussian orthogonal case, there is no such time scale and the integral falls off inversely proportional to time.     

Adaptive fuzzy nonlinear inversion-based control for uncertain chaotic systems

<正>This paper presents a robust output feedback control method for uncertain chaotic systems,which comprises a nonlinear inversion-based controller with a fuzzy robust compensator.The proposed controller eliminates the unknown nonlinear function by using a fuzzy system,whose inputs are not the state variables but feedback error signals.The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique.The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems.Theoretical results are illustrated through two simulation examples.     

Adaptive tracking control for a class of uncertain chaotic systems

The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs.Based on the adaptive technique,sliding mode control method and pole assignment technique,a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.     

Quantum-mechanical nonperturbative response of driven chaotic mesoscopic systems

Consider a time-dependent Hamiltonian H(Q,P;x(t)) with periodic driving x(t) = Asin(Omegat). It is assumed that the classical dynamics is chaotic, and that its power spectrum extends over some frequency range |omega|A(prt), where A(prt) approximately Planck's over 2pi, the system may have a relatively strong response for Omega>omega(cl) due to QM nonperturbative effect.     

Control of chaotic systems using targeting by extended control regions method

In this work, the previously proposed extended control regions (ECR) algorithm for targeting is improved by using individual neural networks for each activation region. The improved version, which exploits the short time predictability of the chaotic system more efficiently, gives better performance with respect to training time and average reaching time while maintaining the advantages of the previous method. Moreover, the simulation results revealed that the meaningful number of activation regions of the controller using improved ECR is nearly linearly related with the prediction horizon of the chaotic system to be targeted, which can be used as a criterion for choosing the number of activation region.     

Adaptive synchronization between two different chaotic systems with unknown parameters

A unified mathematical expression describing a class of chaotic systems is presented, for which the problem of adaptive synchronization between two different chaotic systems with unknown parameters has been studied. Based on Lyapunov stability theory, an adaptive synchronization controller is designed and analytic expression of the controller and the adaptive laws of parameters are developed. The adaptive synchronizations between Lorenz and Chen systems, a modified Chua's circuit and Rössler systems are taken as two illustrative examples to show the effectiveness of the proposed method.     

Adaptive control and synchronization for chaotic systems with parametric uncertainties

An adaptive control scheme using only part of the system states for the stabilization of one chaotic system and the synchronization of two chaotic systems is presented. The system parameters are allowed to have a large range of time varying uncertainties around their fixed unknown nominal values both in the stabilization and the synchronization control problems. Simulation results also illustrate the effectiveness of the proposed control scheme.     

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 Lü system is used to illustrate the validity of this theoretic method.     

Adaptive generalized projective synchronization in different chaotic systems based on parameter identification

In this Letter, the generalized projective synchronization of different chaotic systems with unknown parameters is investigated. By Lyapunov stability theory, the adaptive control method is proposed to achieve above synchronization phenomenon. Meanwhile, according to the invariance principle of differential equations, unknown parameter can be estimated accurately. The schemes are successfully applied to two groups of examples: the anti-phase synchronization between Lorenz system and Chen system; the complete synchronization between hyper-chaotic system and generalized Loren system. The corresponding numerical results are presented to verify the effectiveness of this method.