Sampled-Data Synchronization of Markovian Coupled Neural Networks With Mode Delays Based on Mode-Dependent LKF

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.

Synchronization of Stochastic Neural Networks Using Looped-Lyapunov Functional and Its Application to Secure Communication

This study aims to investigate the synchronization of user-controlled and uncontrolled neural networks (NNs) that exhibit chaotic solutions. The idea behind focusing on synchronization problems is to design the user-desired NNs by emulating the dynamical properties of traditional NNs rather than redefining them. Besides, instead of conventional NNs, this study considers NNs with significant factors such as time-dependent delays and uncertainties in the neural coefficients. In addition, information transmission over transmission may experience stochastic disturbances and network transmission. These factors will result in a stochastic differential NN model. Analyzing the NNs without these factors may be incompatible during the implementation. Theoretically, the model with stochastic disturbances can be considered a stochastic differential model, and the stability conditions are derived by employing Itô's formula and appropriate integral inequalities. To achieve synchronization, the sampled-data-based control scheme is proposed because it is more effective while information is being transmitted over networks. In contrast to the existing studies, this study contributes in terms of handling stochastic disturbances, effects of time-varying delays, and uncertainties in the system parameters via looped-type Lyapunov functional. Besides this, in the application view, delayed NNs are employed as a cryptosystem that helps to secure the transmission between the sender and the receiver, which is explored by illustrating the statistical measures evaluated for the standard images. From the simulation results, the proposed control and derived sufficient conditions can provide better synchronization and the proposed delayed NNs give a better cryptosystem.

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.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Dissipativity-Based Finite-Time Filtering for Uncertain Semi-Markovian Jump Random Systems With Multiple Time Delays and State Constraints

This article is concerned with the issue of dissipativity-based finite-time multiple delay-dependent filtering for uncertain semi-Markovian jump random nonlinear systems with state constraints. There are multiple time-varying delays, nonlinear functions, and intermittent faults (IFs) in the systems. This is one of the few attempts for the issue studied in this article. First, a filter is designed for the uncertain semi-Markovian jump random nonlinear systems. An augmented system with regard to the resulting filtering error is acquired. Then, sufficient conditions of the augmented system are generated by the stochastic Lyapunov function. Finite-time boundedness (FTB) and input-output finite-time mean square stabilization (IO-FTMSS) are both realized. The effectiveness and feasibility of the method are rendered via three examples.

Finite-Time Output Synchronization and H∞ Output Synchronization of Coupled Neural Networks With Multiple Output Couplings

This article investigates the finite-time output synchronization and H_∞ output synchronization problems for coupled neural networks with multiple output couplings (CNNMOC), respectively. By choosing appropriate state feedback controllers, several finite-time output synchronization and H_∞ output synchronization criteria are proposed for the CNNMOC. Moreover, a coupling-weight adjustment scheme is also developed to guarantee the finite-time output synchronization and H_∞ output synchronization of CNNMOC. Finally, two numerical examples are given to verify the effectiveness of the presented criteria.

Finite-Time Output Synchronization of Undirected and Directed Coupled Neural Networks With Output Coupling

This article focuses on the finite-time output synchronization problem for undirected and directed coupled neural networks with output coupling (CNNOC). Based on the designed state feedback controllers and some inequality techniques, we present several finite-time output synchronization criteria for these network models. In addition, two kinds of coupling-weight adjustment strategies are also developed to guarantee the finite-time output synchronization of undirected and directed CNNOC. Finally, two numerical examples are also provided to demonstrate the effectiveness of the theoretical results.

Synchronization criteria of delayed inertial neural networks with generally Markovian jumping

In this paper, the synchronization problem of inertial neural networks with time-varying delays and generally Markovian jumping is investigated. The second order differential equations are transformed into the first-order differential equations by utilizing the variable transformation method. The Markovian process in the systems is uncertain or partially known due to the delay of data transmission channel or the loss of data information, which is more general and practicable to consider generally Markovian jumping inertial neural networks. The synchronization criteria can be obtained by using the delay-dependent Lyapunov-Krasovskii functionals and higher order polynomial based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, the numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

Relaxed Stability Criteria for Neural Networks With Time-Varying Delay Using Extended Secondary Delay Partitioning and Equivalent Reciprocal Convex Combination Techniques

This article investigates global asymptotic stability for neural networks (NNs) with time-varying delay, which is differentiable and uniformly bounded, and the delay derivative exists and is upper-bounded. First, we propose the extended secondary delay partitioning technique to construct the novel Lyapunov-Krasovskii functional, where both single-integral and double-integral state variables are considered, while the single-integral ones are only solved by the traditional secondary delay partitioning. Second, a novel free-weight matrix equality (FWME) is presented to resolve the reciprocal convex combination problem equivalently and directly without Schur complement, which eliminates the need of positive definite matrices, and is less conservative and restrictive compared with various improved reciprocal convex inequalities. Furthermore, by the present extended secondary delay partitioning, equivalent reciprocal convex combination technique, and Bessel-Legendre inequality, two different relaxed sufficient conditions ensuring global asymptotic stability for NNs are obtained, for time-varying delays, respectively, with unknown and known lower bounds of the delay derivative. Finally, two examples are given to illustrate the superiority and effectiveness of the presented method.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Distributed Dissipative State Estimation for Markov Jump Genetic Regulatory Networks Subject to Round-Robin Scheduling

The distributed dissipative state estimation issue of Markov jump genetic regulatory networks subject to round-robin scheduling is investigated in this paper. The system parameters randomly change in the light of a Markov chain. Each node in sensor networks communicates with its neighboring nodes in view of the prescribed network topology graph. The round-robin scheduling is employed to arrange the transmission order to lessen the likelihood of the occurrence of data collisions. The main goal of the work is to design a compatible distributed estimator to assure that the distributed error system is strictly (Λ ₁,Λ ₂,Λ ₃) - γ -stochastically dissipative. By applying the Lyapunov stability theory and a modified matrix decoupling way, sufficient conditions are derived by solving some convex optimization problems. An illustrative example is given to verify the validity of the provided method.

Finite-Time Passivity and Synchronization of Coupled Reaction-Diffusion Neural Networks With Multiple Weights

In this paper, two multiple weighted coupled reaction-diffusion neural networks (CRDNNs) with and without coupling delays are introduced. On the one hand, some finite-time passivity (FTP) concepts are proposed for the spatially and temporally system with different dimensions of output and input. By choosing appropriate Lyapunov functionals and controllers, several sufficient conditions are presented to ensure the FTP of these CRDNNs. On the other hand, the finite-time synchronization (FTS) problem is also discussed for the multiple weighted CRDNNs with and without coupling delays, respectively. Finally, two numeral examples with simulation results are provided to verify the effectiveness of the obtained FTP and FTS criteria.

Generalized State Estimation for Markovian Coupled Networks Under Round-Robin Protocol and Redundant Channels

In this paper, the problem of generalized state estimation for an array of Markovian coupled networks under the round-Robin protocol (RRP) and redundant channels is investigated by using an extended dissipative property. The randomly varying coupling of the networks under consideration is governed by a Markov chain. With the aid of using the RRP, the transmission order of nodes is availably orchestrated. In this case, the probability of occurrence data collisions through a shared constrained network may be reduced. The redundant channels are also used in the signal transmission to deal with the frangibility of networks caused by a single channel in the networks. The network induced phenomena, that is, randomly occurring packet dropouts and randomly occurring quantization are fully considered. The main purpose of the research is to find a desired estimator design approach such that the extended (Ω₁,Ω₂,Ω₃) - γ -stochastic dissipativity property of the estimation error system is guaranteed. In terms of the Lyapunov-Krasovskii methodology, the Kronecker product and an improved matrix decoupling approach, sufficient conditions for such an addressed problem are established by means of handling some convex optimization problems. Finally, the serviceability of the proposed method is explained by providing an illustrated example.

Finite-Time Synchronization of Coupled Hierarchical Hybrid Neural Networks With Time-Varying Delays

This paper is concerned with the finite-time synchronization problem of coupled hierarchical hybrid delayed neural networks. This coupled hierarchical hybrid neural networks consist of a higher level switching and a lower level Markovian jumping. The time-varying delays are dependent on not only switching signal but also jumping mode. By using a less conservative weighted integral inequality and stochastic multiple Lyapunov-Krasovskii functional, new finite-time synchronization criteria are obtained, which makes the state trajectories be kept within the prescribed bound in a time interval. Finally, an example is proposed to demonstrate the effectiveness of the obtained results.