Adaptive Impulsive Synchronization Research Articles

Adaptive impulsive synchronization for fractional-order quaternion-valued neural networks with different structures and unknown parameters

The synchronization issue between fractional-order quaternion-valued neural networks with different structures is more common than that with the same structure in the real world. This paper addresses the Mittag-Leffler stability and adaptive impulsive synchronization between two fractional-order quaternion-valued neural networks with different structures. We also propose two assumptions to analyze the parameters of the nonlinear activation functions. Based on the Mittag-Leffler stability and fractional-order Lyapunov direct method, an impulsive controller scheme is designed to ensure the global stability of fractional-order time-delay quaternion-valued neural networks. We also analyzed the situation when the self-feedback matrix and connection matrix of quaternion-valued fractional-order neural networks with different structures are unknown and designed adaptive impulsive controllers to achieve synchronization. Finally, we verified the feasibility and effectiveness of the proposed theorem through numerical simulation experiments.

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Fractional order quaternion‐valued neural networks are a type of fractional order neural networks for which neuron state, synaptic connection strengths, and neuron activation functions are quaternion. This paper is dealing with the Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. The fractional order quaternion‐valued neural networks are separated into four real‐valued systems forming an equivalent four real‐valued fractional order neural networks, which decreases the computational complexity by avoiding the noncommutativity of quaternion multiplication. Via some fractional inequality techniques and suitable Lyapunov functional, a brand new criterion is proposed first to ensure the Mittag‐Leffler stability for the addressed neural networks. Besides, the combination of quaternion‐valued adaptive and impulsive control is intended to realize the asymptotically synchronization between two fractional order quaternion‐valued neural networks. Ultimately, two numerical simulations are provided to check the accuracy and validity of our obtained theoretical results.

A survey on complex dynamical networks with impulsive effects

We review the research on complex dynamical networks (CDNs) with impulsive effects. We provide a comprehensive and intuitive overview of the fundamental results and recent progress of CDNs with impulsive effects, where impulsive effects are considered from two aspects, i.e., impulsive control and impulsive perturbation. Five aspects of CDNs with impulsive effects are surveyed, including synchronizing impulses, desynchronizing impulses, adaptive-impulsive synchronization, pinning impulsive synchronization, and CDNs with stochastic and impulsive effects. Finally, conclusions and some future research directions are briefly addressed.

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

Adaptive impulsive cluster synchronization in community network with nonidentical nodes

In this paper, cluster synchronization in community network with nonidentical nodes is investigated. Through introducing proper adaptive strategy into impulsive control scheme, adaptive impulsive controllers are designed for achieving the cluster synchronization. In this adaptive impulsive control scheme, for any given networks, the impulsive gains can adjust themselves to proper values according to the proposed adaptive strategy when the impulsive intervals are fixed. The impulsive instants can be estimated by solving a sequence of maximum value problems when the impulsive gains are fixed. Both community networks without and with coupling delay are considered. Based on the Lyapunov function method and mathematical analysis technique, two synchronization criteria are derived. Several numerical examples are performed to verify the effectiveness of the derived theoretical results.

A novel adaptive-impulsive synchronization of fractional-order chaotic systems**Project supported by the National Natural Science Foundations of China (Grant Nos. 11161027 and 11262009), the Key Natural Science Foundation of Gansu Province, China (Grant No. 1104WCGA195), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136204110001).

A novel adaptive–impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors’ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive–impulsive control scheme.

Parameter identification and adaptive–impulsive synchronization of uncertain complex networks with nonidentical topological structures

In this paper, we integrate impulsive control and adaptive control methods, based on the stability theory of impulsive differential equations, synchronization of uncertain complex networks with nonidentical topological structures is investigated. By designing effective adaptive–impulsive controllers, we achieve synchronization criteria of uncertain complex networks with nonidentical topological structures, parameter identification is realized simultaneously as the synchronization occurs. Moreover, the case of identical topological structures is considered. Finally, numerical simulations are given to illustrate the theoretical results.

Adaptive impulsive synchronization of fractional order chaotic system with uncertain and unknown parameters

Impulsive synchronization for fractional order chaotic system is a difficult problem that is required to solve. In this paper, a new method to realize the adaptive impulsive synchronization of two general fractional order chaotic systems with uncertain and unknown parameters is investigated. A new function is to be applied to the stability theory of fractional order directly. Then the impulsive synchronization of two fractional order chaotic systems with unknown parameters is discussed. The criteria for synchronization of the systems are established. Finally, some numerical examples are delivered to illustrate the effectiveness of our results.

Adaptive–impulsive synchronization and parameters estimation of chaotic systems with unknown parameters by using discontinuous drive signals

In this paper, adaptive–impulsive synchronization and parameters estimation of chaotic systems only by using discontinuous drive signals are investigated. In the scheme proposed both the impulsive synchronization controller and the adaptive parameters update law are modeled only by using discontinuous output of the chaotic system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. This is meaningful in applications when continuous signals cannot be obtained. Moreover, concrete schemes are designed for quantum cellular neural network (Quantum-CNN) and well known Chen chaotic system. Results show that synchronization and the parameters estimation can be achieved under some conditions. The numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.

Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discrete‐time drive signals

This article investigates the adaptive impulsive synchronization of delayed chaotic system with full unknown parameters. Aiming at this problem, we propose a new adaptive strategy, in which both the adaptive–impulsive controller and the parameters adaptive laws are designed via the discrete‐time signals from the drive system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. Moreover, the concrete adaptive strategies are achieved for delayed Hopfield neural network, optical Ikeda system and the well‐known delayed Lü chaotic system. As expected, numerical simulations show the effectiveness of the proposed strategy. This method has potential applications in parameters estimation, secure communication, and cryptanalysis when only discrete signals are transmitted in communication channel. © 2014 Wiley Periodicals, Inc. Complexity 21: 43–51, 2016

New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems

This paper studies the robust adaptive-impulsive synchronization in chaotic delayed neural networks with uncertainties. For this class of complex networks, some simple adaptive-impulsive controllers with updated strengths are designed. Using the well-known extended Halany inequality and Lyapunov functions, several less conservative conditions are obtained compared with the existing results. The simulation results show that the proposed results are effective.

Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method.

Erratum to: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems

Erratum to: Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems

Adaptive impulsive synchronization of uncertain drive-response complex-variable chaotic systems

In this paper, impulsive synchronization of drive-response complex-variable chaotic systems is investigated. The drive-response systems with known parameters is considered via impulsive control and adaptive scheme as well as systems with unknown parameters. Noticeably, adaptive strategy is adopted to relax the restriction on the impulsive interval, and the system parameters need not to be known beforehand. According to the Lyapunov stability theory, some synchronization criteria are derived and verified by several numerical simulations.

Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems

Synchronization of nonlinear dynamical systems with complex variables has attracted much more attention in various fields of science and engineering. In this paper, the problem of parameter identification and adaptive impulsive synchronization for a class of chaotic (hyperchaotic) complex nonlinear systems with uncertain parameters is investigated. Based on the theories of adaptive control and impulsive control, a synchronization scheme is designed to make a class of chaotic and hyperchaotic complex systems asymptotically synchronized, and uncertain parameters are identified simultaneously in the process of synchronization. Particularly, the proposed adaptive–impulsive control laws for synchronization are simple and can be readily applied in practical applications. The synchronization of two identical chaotic complex Chen systems and two identical hyperchaotic complex Lu systems are taken as two examples to verify the feasibility and effectiveness of the proposed controllers and identifiers.

Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

The impulsive synchronization and adaptive-impulsive synchronization of a novel financial hyperchaotic system are investigated. Based on comparing principle for impulsive functional differential equations, several sufficient conditions for impulsive synchronization are derived, and the upper bounds of impulsive interval for stable synchronization are estimated. Furthermore, a nonlinear adaptive-impulsive control scheme is designed to synchronize the financial system using invariant principle of impulsive dynamical systems. Moreover, corresponding numerical simulations are presented to illustrate the effectiveness and feasibility of the proposed methods.

Adaptive impulsive synchronization of a class of chaotic and hyperchaotic systems

In this paper, the issue of synchronization and parameter identification for a class of chaotic and hyperchaotic systems is discussed. Based on the theories of adaptive control and impulsive control, a synchronization scheme is developed to achieve complete synchronization and parameter identification of a class of chaotic and hyperchaotic systems for the first time. Sufficient conditions are derived to synchronize the systems with different impulse distances. The bounds of the stable regions are also estimated. Numerical examples are presented to demonstrate the effectiveness of the proposed controllers and identifiers.

Adaptive impulsive synchronization of nonlinear chaotic systems

In this paper, an adaptive impulse control with only one restriction criterion is derived to achieve synchronization of nonlinear chaotic systems in the exponential rate of convergence. It is assumed that the system satisfies the local Lipschitz condition and the Lipschitz constant is estimated by an augmented adaptation equation. The significance of the related control parameters in the criterion is also discussed in detail. The Duffing and the Lorenz systems have been simulated to illustrate the theoretical analysis.

Adaptive–impulsive synchronization of chaotic systems

Abstract In this paper, we investigate nonlinear adaptive–impulsive synchronization of chaotic systems. The core of adaptive–impulsive synchronization of chaotic systems is to design suitable nonlinear adaptive–impulsive controllers to attain certain aims. Based on invariant principle of impulsive dynamical systems, nonlinear adaptive–impulsive controllers are derived to make the state of chaotic systems synchronized. Accordingly, concrete nonlinear adaptive–impulsive control scheme is designed for quantum cellular neural network (Quantum-CNN). Moreover, numerical simulations are presented to illustrate the effectiveness of the proposed nonlinear controllers, which is more effective than that in the previous literature.

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.