Synchronization Problem Of Neural Networks Research Articles

Delayed Impulsive Control for Lag Synchronization of Delayed Neural Networks Involving Partial Unmeasurable States.

In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main results.

Finite-Time Synchronization for Stochastic Fractional-Order Memristive BAM Neural Networks with Multiple Delays

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

Synchronization control of Markov jump neural networks with mixed time-varying delay and parameter uncertain based on sample point controller

This paper put forward an improved synchronization problem for neural networks with Markov jump parameters. The traditional Markov jump neural network (MJNN) only considers the basic external time-varying delays, ignoring both the distributed and leakage delays in the internal transmission of the neural network and the small time-varying errors in the mode switching of Markov probability transition rates. In this paper, we focus on the synchronization of MJNN with mixed time-varying delay. And an improved Lyapunov–Krasovskii functional is constructed. The convergence of inequalities is solved by using affine Bessel–Legendre inequalities and Wirtinger double integral inequalities. At the same time, a new method is used to optimize the mathematical geometric area of the time-varying delay and reduce the conservativeness of the system. Finally, a sample point controller is constructed to synchronize the driving system and the corresponding system.

Exponential Synchronization of Neural Networks With Time-Varying Delays via Dynamic Intermittent Output Feedback Control

This paper addresses the exponential synchronization problem for neural networks with time-varying delays. First, a novel controller is presented by combining intermittent control with dynamic output feedback control. Next, a sufficient criterion is established based on the Lyapunov-Krasovskii functional approach and the lower bound lemma for reciprocally convex technique to ensure exponential stability of the resultant closed-loop system. Then, some solvable conditions of the proposed control problem are derived in terms of linear matrix inequalities. Notably, our results here extend the existing ones to the relaxed case because the derivative of time-varying delays is now an arbitrary bounded real number. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed method.

Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings

This paper presents the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling. The function projective synchronization of this model via hybrid adaptive pinning controls and hybrid adaptive controls, composed of nonlinear and adaptive linear feedback control, is further investigated in this study. Based on Lyapunov stability theory combined with the method of the adaptive control and pinning control, some novel and simple sufficient conditions are derived for the function projective synchronization problem of neural networks with mixed time-varying delays and uncertainties asymmetric coupling, and the derived results are less conservative. Particularly, the control method focuses on how to determine a set of pinned nodes with fixed coupling matrices and strength values and randomly select pinning nodes. Based on adaptive control technique, the parameter update law, and the technique of dealing with some integral terms, the control may be used to manipulate the scaling functions such that the drive system and response systems could be synchronized up to the desired scaling function. Finally, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control

In this paper, the synchronization problem for neural networks with stochastic perturbation is studied with intermittent control via adaptive aperiodicity. Under the framework of stochastic theory and Lyapunov stability method, we develop some techniques of intermittent control with adaptive aperiodicity to achieve the synchronization of a class of neural networks, modeled by stochastic systems. Some effective sufficient conditions are established for the realization of synchronization of the underlying network. Numerical simulations of two examples are provided to illustrate the theoretical results obtained in the paper.

Synchronization of Neural Networks with Mixed Time Delays under Information Constraints

This paper investigates the synchronization problem of neural networks with mixed time delays under information constrains. The designed synchronization scheme is built on the framework of hybrid systems. Besides including nonuniform sampling, some other characteristics, such as quantization, transmission-induced delays, and data packet dropouts, are also considered. The sufficient condition that depended on network characteristics is obtained to guarantee the remote asymptotical synchronization of neural networks with mixed time delays. A numerical example is given to illustrate the validity of the proposed method.

Synchronization of Chaotic Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Sampled-Data Control

This paper investigates the synchronization problem for neural networks with leakage delay and both discrete and distributed time-varying delays under sampled-data control. By employing the Lyapunov functional method and using the matrix inequality techniques, a delay-dependent LMIs criterion is given to ensure that the master systems and the slave systems are synchronous. An example with simulations is given to show the effectiveness of the proposed criterion.

Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays

This paper considers the chaotic synchronization problem of neural networks with time-varying and distributed delays using impulsive control method. By utilizing the stability theory for impulsive functional differential equations, several impulsive control laws are derived to guarantee the exponential synchronization of neural networks with time-varying and distributed delays. It is shown that chaotic synchronization of the networks is heavily dependent on the designed impulsive controllers. Moreover, these conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. Finally, a numerical example and its simulation are given to show the effectiveness and advantage of the proposed control schemes.

Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data

This paper investigates the synchronization problem of neural networks with time-varying delay under sampled-data control in the presence of a constant input delay. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. A simple and less conservative synchronization criterion is given to ensure the master systems synchronize with the slave systems by using the linear matrix inequality (LMI) approach. The design method of the desired sampled-data controller is also proposed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.