Synchronization Of Chaotic Neural Networks Research Articles

Improved criteria of sampled-data master-slave synchronization for chaotic neural networks with actuator saturation

This paper investigates the sampled-data master-slave synchronization problem for chaotic neural networks with actuator saturation by constructing novel Lyapunov-Krasovskii functionals. The proposed functionals exploit the sampling interval from the recent sampling instant tk to the next sampling instant tk+1 by using the integral vectors ∫tkte(s)ds, 2t−tk∫tkt∫tkse(u)duds, ∫ttk+1e(s)ds, and 2tk+1−t∫ttk+1∫stk+1e(u)duds. Based on the proposed functionals, this paper derives sufficient criteria for the sampled-data master-slave synchronization of chaotic neural networks with actuator saturation represented using a dead zone nonlinearity. Also, the controller gain matrix of the sampled-data controller can be obtained by solving linear matrix inequalities (LMIs). The superiority and validity of the proposed criterion are verified through the numerical example obtained from the literature.

Synchronization of Chaotic Neural Networks: Average-Delay Impulsive Control.

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.

Regional sampled-data synchronization of chaotic neural networks using piecewise-continuous delay dependent Lyapunov functional

In this paper, a regional sampled-data synchronization criterion is proposed for the chaotic neural networks (CNNs) with input saturation using the piecewise-continuous delay dependent Lyapunov functional (PDDLF) approach. The aim of this work is to enlarge the region of attraction (ROA) of the synchronous state for CNNs with input saturation. Unlike existing works, the Lyapunov functional in the proposed approach is constructed from a polynomial with respect to the piecewise-continuous delay. Moreover, the proposed Lyapunov functional is combined with looped-functionals to derive the sufficient condition. The synchronization criterion is formulated in terms of sum of squares (SOS) programs, which reduces the infinite-dimensional linear matrix inequality (LMI) conditions to a finite number of SOS conditions. A numerical example is presented to illustrate the effectiveness and advantages of the proposed approach.

Quantized control for extended dissipative synchronization of chaotic neural networks: A discretized LKF method

This work focuses on the extended dissipative synchronization problem for chaotic neural networks with time delay under quantized control. The discretized Lyapunov–Krasovskii functional method, in combination with the free-weighting matrix approach, is employed to obtain an analysis result of the extended dissipativity with low conservatism. Then, with the help of several decoupling methods, a computationally tractable design approach is proposed for the needed quantized controller. Finally, two examples are provided to illustrate the usefulness of the present analysis and design methods, respectively.

Quantization synchronization of chaotic neural networks with time delay under event-triggered strategy.

This paper shows solicitude for the quantization synchronization of delayed chaotic master and slave neural networks under an dynamic event-triggered strategy. In virtue of a generalized Halanay-type inequality, a theoretical criterion for quasi-synchronization of master and slave neural networks is derived. Meanwhile, we can obtain an exact upper bound of synchronization error by using this criterion. Compared with output feedback controller with event triggering and quantization, the case where the controller only affected by quantization is also considered. Then, we exclude the Zeno behavior of the event-triggered controller. A sufficient criterion for the existence of the quantized output feedback controllers is also provided. A numerical example is cited to illustrate the efficiency of our theoretical criteria. In addition, some experiments of secure image communication are conducted under quasi-synchronization of master and slave neural networks.

Finite-time synchronization for chaotic neural networks with stochastic disturbances

In this paper, we focus on the problem of synchronization for chaotic neural networks with stochastic disturbances. Firstly, we provide a basic result that the systems including the drive system, response system, and error system have a unique solution on the whole time horizon. Based on this result, we design a new control law such that the response system can be synchronized with the drive chaotic system in finite time. Furthermore, we show that the settling time is independent of the initial data under some proper conditions, which hints that the fixed-time synchronization of chaotic neural networks can be realized by our proposed method. Finally, we give simulations to verify the theoretical analysis for our main results.

Augmented two-side-looped Lyapunov functional for sampled-data-based synchronization of chaotic neural networks with actuator saturation

This paper further investigated the synchronization problem of the chaotic neural networks by utilizing the sampled-data control with actuator saturation. Firstly, an augmented two-side-looped Lyapunov functional including both the states of the error system and their derivative is constructed. Then the Wirtinger-based integral inequality in combination with the improved reciprocally convex matrix inequality is applied to estimate the derivative of the presented Lyapunov functional and improved synchronization criteria are derived. As a result, a state feedback controller based on sampled-data is designed, making the drive system synchronize with the response system. Finally, through the results of the numerical example, the validity and superiority of the proposed methods have been confirmed.

Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances

<p style='text-indent:20px;'>This paper investigates the delay-distribution-dependent exponential synchronization problem for a class of chaotic neural networks with mixed random time-varying delays as well as restricted disturbances. Given the probability distribution of the time-varying delay, stochastic variable that satisfying Bernoulli distribution is formulated to produce a new system which includes the information of the probability distribution. Based on the Lyapunov-Krasovskii functional method, the Jensen's integral inequality theory and linear matrix inequality (LMI) technique, several delay-distribution-dependent sufficient conditions are developed to guarantee that the chaotic neural networks with mixed random time-varying delays are exponentially synchronized in mean square. Furthermore, the derived results are given in terms of simplified LMI, which can be straightforwardly solved by Matlab. Finally, two numerical examples are proposed to demonstrate the feasibility and the effectiveness of the presented synchronization scheme.

Impulsive Synchronization of Delayed Chaotic Neural Networks With Actuator Saturation

This article focuses on the impulsive synchronization of chaotic neural networks (CNNs) with time-varying delays subject to actuator saturation. By constructing discontinuous Lyapunov function and employing linear matrix inequality (LMI) approach, some sufficient conditions are derived to guarantee the synchronization object of the delayed chaotic neural networks. In addition, the control methods in this article have no strict requirements on the size of time delay and the actuator saturation domain, which is more flexible and practical in real system. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Secure Communication Based on Quantized Synchronization of Chaotic Neural Networks Under an Event-Triggered Strategy.

This article presents a secure communication scheme based on the quantized synchronization of master-slave neural networks under an event-triggered strategy. First, a dynamic event-triggered strategy is proposed based on a quantized output feedback, for which a quantized output feedback controller is formed. Second, theoretical criteria are derived to ensure the bounded synchronization of master-slave neural networks. With these criteria, an explicit upper bound is given for the synchronization error. Sufficient conditions are also provided on the existence of quantized output feedback controllers. A Chua's circuit is chosen to illustrate the effectiveness of our theoretical results. Third, a secure communication scheme is presented based on the synchronization of master-slave neural networks by combining the basic principle of cryptology. Then, a secure image communication is studied to verify the feasibility and security performance of the proposed secure communication scheme. The impact of the quantization level and the event-triggered control (ETC) on image decryption is investigated through experiments.

Synchronization of chaotic neural networks with time delay via distributed delayed impulsive control

This letter investigates the impulsive synchronization of chaotic neural networks with time delays. A novel impulsive delayed inequality is proposed, where the control effect of distributed delayed impulses is fully considered. Based on the inequality, a distributed delayed impulsive controller is proposed for exponential synchronization of chaotic neural networks. Finally, numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

Observer-based sliding mode control for synchronization of delayed chaotic neural networks with unknown disturbance

This paper considers the synchronization of delayed chaotic neural networks with unknown disturbance via observer-based sliding mode control. We design a sliding surface involving integral structure and a discontinuous control law such that the trajectories of error system converge to the sliding surface in finite time and remain on it thereafter. Then, by constructing Lyapunov–Krasovskii functional and using the linear matrix inequality (LMI) technique, some sufficient conditions are derived to guarantee the synchronization of chaotic neural networks. The advantages of our proposed results include:(i) It can be applied to synchronous control for drive and response systems with different structures; (ii) It can be applied to the response system with unknown disturbance. Finally, a simulation example is shown to illustrate the proposed methods.

Uniform Quantized Synchronization for Chaotic Neural Networks with Successive Packet Dropouts

AbstractIn this paper, the problem of uniform quantized synchronization is investigated for chaotic neural networks with packet dropouts. By means of the stochastic analysis approach and inequality technique, sufficient conditions are derived under which the synchronization error system is exponentially ultimately bounded in mean square. Finally, a numerical example is provided to validate the feasibility and effectiveness of the proposed results.

Global power-rate synchronization of chaotic neural networks with proportional delay via impulsive control

Abstract This paper considers the problem of global power-rate synchronization of chaotic neural networks with proportional delay via impulsive control. By establishing a novel impulsive delayed differential inequality, some delay-dependent impulsive controlled laws are derived to guarantee the global power-rate synchronization of chaotic neural networks with proportional delay. Two examples with numerical simulations are given to illustrate the feasibility and advantage of the proposed control schemes.

Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control.

In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.

Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control

In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into account. By constructing a proper Lyapunov function and employing the impulsive control theory, some sufficient conditions for lag synchronization of the addressed chaotic neural networks are derived in terms of linear matrix inequalities (LMIs). The hybrid controller including sampled-data controller and impulsive controller is designed based on the established LMIs. A numerical example is provided to demonstrate the effectiveness and advantage of the obtained results.

Exponential synchronization of chaotic neural networks with time-varying delay via intermittent output feedback approach

This paper is dealt with the problem of exponential synchronization for chaotic neural networks with time-varying delay by using intermittent output feedback control. Based on the Lyapunov–Krasovskii functional method and the lower bound lemma for reciprocally convex technique, a novel criterion for existence of the controller is first established to ensure synchronization between the master and slave systems. Moreover, from the delay point of view, the derived criterion is extended to the relaxed case because of introducing an adjustable parameter in the Lyapunov–Krasovskii functional. Finally, a numerical simulation is carried out to demonstrate the effectiveness of the proposed synchronization law.

Wirtinger-based multiple integral inequality approach to synchronization of stochastic neural networks

This paper investigates the synchronization problem for a class of chaotic neural networks with discrete and unbounded distributed time delays under stochastic perturbations. Firstly, based on the Wirtinger-based double integral inequality, two novel inequalities are proposed, which are multiple integral forms of the Wirtinger-based integral inequality. Next, by applying the Jensen-type integral inequality for stochastic case and combining the Jensen integral inequality with the reciprocally convex combination approach, a delay-dependent criterion is developed to achieve the synchronization for the stochastic chaotic neural networks in the sense of mean square. In the case of no stochastic perturbations, by applying the reciprocally convex combination approach for high order case and a free-matrix-based inequality, novel delay-dependent conditions are established to achieve the synchronization for the chaotic neural networks. All the results are based on dividing the bounding of activation function into two subintervals with equal length. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Delay-dependent H∞ synchronization for chaotic neural networks with network-induced delays and packet dropouts

This paper investigates the problem of H∞ synchronization for chaotic neural networks with network-induced delays and packet dropouts. A novel master–slave synchronization scheme is established where the network-induced delays and data packet dropouts are taken into consideration. By constructing the Lyapunov functional and employing the Wirtinger-based integral inequality, several delay-dependent conditions are obtained to guarantee that the error system is globally asymptotically stable and satisfies a prescribed H∞ performance constraint. Finally, two numerical examples are presented to validate the feasibility and effectiveness of the results derived.

Adaptive observer-based projective synchronization for chaotic neural networks with mixed time delays

This paper addresses adaptive projective synchronization of chaotic neural networks with mixed time delays based on an observer-based design strategy. For this, the idea of designing nonlinear state observers is used, and a novel adaptive observer-based controller is given to provide projective synchronization between the master and the slave chaotic systems. Lyapunov theorem is also utilized to obtain the adaptation laws for tuning the controller when the parameters of the master system are unknown. The proposed control scheme is successfully applied for projective synchronization of two chaotic neural networks with mixed delays. The simulation results demonstrate the feasibility and efficiency of the presented method.