Synchronization of Inertial Neural Networks With Time-Varying Delays via Quantized Sampled-Data Control

Aperiodically intermittent quantized control-based exponential synchronization of quaternion-valued inertial neural networks

Inertial neural networks are proposed via introducing an inertia term into the Hopfield models, which make their dynamic behavior more complex compared to the traditional first-order models. Besides, the aperiodically intermittent quantized control over conventional feedback control has its potential advantages on reducing communication blocking and saving control cost. Based on these facts, we are mainly devoted to exploring of exponential synchronization of quaternion-valued inertial neural networks under aperiodically intermittent quantized control. Firstly, a compact quaternion-valued aperiodically intermittent quantized control protocol is developed, which can mitigate significantly the complexity of theoretical derivation. Subsequently, several concise criteria involving matrix inequalities are formulated through constructing a type of Lyapunov functional and employing a direct analysis approach. The correctness of the obtained results eventually is verified by a typical example.

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Fixed-Time Stability of Nonlinear Impulsive Systems and its Application to Inertial Neural Networks

This article is concerned with the fixed-time stability (FTS) problem of nonlinear impulsive systems (NISs). By means of the impulsive control mechanism and Lyapunov functions theory, several sufficient conditions are established to ensure the FTS of general NISs. Meanwhile, some novel impulse-dependent settling-time estimation schemes are developed, which fully considers the influence of stabilizing impulses and destabilizing impulses on the convergence rate of the system states. The proposed schemes establish a quantitative relationship between the upper bound of the settling time and impulse effects. It shows that stabilizing impulses can accelerate the convergence rate of the system states and leads to the upper bound of the settling time being smaller. Conversely, destabilizing impulses can reduce it and make the upper bound of the settling time larger. Then, the theoretical results are applied to delayed inertial neural networks (DINNs), where two kinds of controllers are designed to realize fixed-time synchronization of the considered systems in the impulse sense. Finally, some numerical examples are provided to illustrate the validity of the proposed theoretical results.

Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling

In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.

Synchronization of Generally Uncertain Markovian Inertial Neural Networks With Random Connection Weight Strengths and Image Encryption Application

This article focuses on the synchronization problem of delayed inertial neural networks (INNs) with generally uncertain Markovian jumping and their applications in image encryption. The random connection weight strengths and generally uncertain Markovian are discussed in the INNs model. Compared with most existing INNs models that have constant connection weight strengths, our model is more practical because connection weight strengths of INNs may randomly vary due to the external and internal environment and human factor. The delay-range-dependent synchronization conditions (DRDSCs) could be obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, two examples are shown to demonstrate the effectiveness of the proposed results.