Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topology via an Adaptive Approach

Outer synchronization and outer H∞ synchronization for coupled fractional-order reaction-diffusion neural networks with multiweights

This paper introduces multiple state or spatial-diffusion coupled fractional-order reaction-diffusion neural networks, and discusses the outer synchronization and outer H∞ synchronization problems for these coupled fractional-order reaction-diffusion neural networks (CFRNNs). The Lyapunov functional method, Laplace transform and inequality techniques are utilized to obtain some outer synchronization conditions for CFRNNs. Moreover, some criteria are also provided to make sure the outer H∞ synchronization of CFRNNs. Finally, the derived outer and outer H∞ synchronization conditions are validated on the basis of two numerical examples.

Event-triggered impulsive cluster synchronization of coupled reaction-diffusion neural networks and its application to image encryption

This paper investigates the cluster synchronization of coupled neural networks with reaction-diffusion terms. With the help of impulsive control strategies, some cluster synchronization criteria are proposed by an appropriate event-triggered mechanism. A numerical example is given to verify the validity of the theoretical results. Additionally, the proposed event-triggered impulsive synchronization is successfully applied to image encryption with encouraging cryptanalysis results demonstrating its strong ability to efficiently encrypt images.

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

Stability of Delayed Reaction-Diffusion Neural-Network Models With Hybrid Impulses via Vector Lyapunov Function

This article focuses on stability analysis of delayed reaction-diffusion neural-network models with hybrid impulses based on the vector Lyapunov function. First, several properties of a vector Halanay-type inequality are given to be the key ingredient for the stability analysis. Then, the Krasovskii-type theorems are established for sufficient conditions of exponential stability, which removes the common threshold of impulses in each neuron subsystem at every impulse time. It shows that the stability of neural networks can be retained with hybrid impulses involved in neural networks, and the synchronization of neural networks can be achieved by designing an impulsive controller, which allows the existence of impulsive perturbation in some nodes and time. Finally, the effectiveness of theoretical results is verified by numerical examples with a successful application to image encryption.

Distributed Adaptive Containment Control for Coupled Reaction-Diffusion Neural Networks With Directed Topology

In this article, we consider the problem of distributed adaptive leader-follower coordination of partial differential systems (i.e., reaction-diffusion neural networks, RDNNs) with directed communication topology in the case of multiple leaders. Different from the dynamical networks with ordinary differential dynamics, the design of adaptive protocols is more difficult due to the existence of spatial variables and nonlinear terms in the model. Under directed networks, a novel adaptive control protocol is proposed to solve the containment control problem of RDNNs. By constructing proper Lyapunov functional and adopting some important prior knowledge, the stability of containment for coupled RDNNs is theoretically proved. Furthermore, a corollary about the leader-follower synchronization with a leader for coupled RDNNs with directed communication topology is given. In the end, two numerical examples are provided to illustrate the obtained theoretical results.

Quantized Sampled-Data Synchronization of Delayed Reaction-Diffusion Neural Networks Under Spatially Point Measurements

This article considers the synchronization problem of delayed reaction-diffusion neural networks via quantized sampled-data (SD) control under spatially point measurements (SPMs), where distributed and discrete delays are considered. The synchronization scheme, which takes into account the communication limitations of quantization and variable sampling, is based on SPMs and only available in a finite number of fixed spatial points. By utilizing inequality techniques and Lyapunov-Krasovskii functional, some synchronization criteria via a quantized SD controller under SPMs are established and presented by linear matrix inequalities, which can ensure the exponential stability of the synchronization error system containing the drive and response dynamics. Finally, two numerical examples are offered to support the proposed quantized SD synchronization method.

Synchronization of memristive neural networks with unknown parameters via event-triggered adaptive control

This paper considers the drive-response synchronization of memristive neural networks (MNNs) with unknown parameters, where the unbounded discrete and bounded distributed time-varying delays are involved. Aiming at the unknown parameters of MNNs, the updating law of weight in response system and the gain of adaptive controller are proposed to realize the synchronization of delayed MNNs. In view of the limited communication and bandwidth, the event-triggered mechanism is introduced to adaptive control, which not only decreases the times of controller update and the amount of data sending out but also enables synchronization when parameters of MNNs are unknown. In addition, a relative threshold strategy, which is relative to fixed threshold strategy, is proposed to increase the inter-execution intervals and to improve the control effect. When the parameters of MNNs are known, the algebraic criteria of synchronization are established via event-triggered state feedback control by exploiting inequality techniques and calculus theorems. Finally, one simulation is presented to validate the effectiveness of the proposed results.

Synchronization of Nonidentical Neural Networks With Unknown Parameters and Diffusion Effects via Robust Adaptive Control Techniques

This paper considers the self-synchronization and tracking synchronization issues for a class of nonidentically coupled neural networks model with unknown parameters and diffusion effects. Using the special structure of neural networks with global Lipschitz activation function, nonidentical terms are treated as external disturbances, which can then be compensated via robust adaptive control techniques. For the case where no common reference trajectory is given in advance, a distributed adaptive controller is proposed to drive the synchronization error to an adjustable bounded area. For the case where a reference trajectory is predesigned, two distributed adaptive controllers are proposed, respectively, to address the tracking synchronization problem with bounded and unbounded reference trajectories, different decomposition methods are given to extract the heterogeneous characteristics. To avoid the appearance of global information, such as the spectrum of the coupling matrix, corresponding adaptive designs on coupling strengths are also provided for both cases. Moreover, the upper bounds of the final synchronization errors can be gradually adjusted according to the parameters of the adaptive designs. Finally, numerical examples are given to test the effectiveness of the control algorithms.

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.

Synchronization of Delayed Neural Networks via Integral-Based Event-Triggered Scheme

This article investigates the event-triggered synchronization of delayed neural networks (NNs). A novel integral-based event-triggered scheme (IETS) is proposed where the integral of the system states, and past triggered data over a period of time are used. With the proposed IETS, the integral event-triggered synchronization problem becomes a distributed delay problem. Using the Bessel-Legendre inequalities, sufficient conditions for the existence of a controller that ensures asymptotic synchronization are provided in the form of linear matrix inequalities (LMIs). Illustrative examples are used to demonstrate the advantages of the proposed IETS method over other event-triggered scheme (ETS) methods. Moreover, this IETS method is applied to the image encryption and decryption. A novel encryption algorithm is proposed to enhance the quality of the encryption process.

Event-Triggered Synchronization for Neutral-Type Semi-Markovian Neural Networks With Partial Mode-Dependent Time-Varying Delays

This article studies the event-triggered stochastic synchronization problem for neutral-type semi-Markovian jump (SMJ) neural networks with partial mode-dependent additive time-varying delays (ATDs), where the SMJ parameters in two ATDs are considered to be not completely the same as the one in the connection weight matrices of the systems. Different from the weak infinitesimal operator of multi-Markov processes, a new one for the double semi-Markovian processes (SMPs) is first proposed. To reduce the conservative of the stability criteria, a generalized reciprocally convex combination inequality (RCCI) is established by the virtue of an interesting technique. Then, based on an eligible stochastic Lyapunov-Krasovski functional, three novel stability criteria for the studied systems are derived by employing the new RCCI and combining with a well-designed event-triggered control scheme. Finally, three numerical examples and one practical engineering example are presented to show the validity of our methods.

Anti-Synchronization in Fixed Time for Discontinuous Reaction-Diffusion Neural Networks With Time-Varying Coefficients and Time Delay

This paper studies the fixed-time anti-synchronization (FTAS) of discontinuous reaction-diffusion neural networks (DRDNNs) with both time-varying coefficients and time delay. First, differential inclusion theory is used to deal with the influence caused by discontinuous activations. In addition, a new fixed-time convergence theorem is used to handle the time-varying coefficients. Second, a novel state-feedback control algorithm and integral state-feedback control algorithm are proposed to realize FTAS of DRDNNs. During the generalized (adaptive) pinning control strategy, a guideline is proposed to select neurons to pin the designed controller. Furthermore, we present several criteria on FTAS by using the generalized Lyapunov function method. Different from the traditional Lyapunov function with negative definite derivative, the derivative of the Lyapunov function can be positive in this paper. Finally, we give two numerical simulations to substantiate the merits of the obtained results.

General decay synchronization and H∞ synchronization of spatial diffusion coupled delayed reaction-diffusion neural networks

This paper deals with the general decay synchronization (GDS) and general decay H_∞ synchronization (GDHS) problems for spatial diffusion coupled delayed reaction-diffusion neural networks (SDCDRDNNs) without and with uncertain parameters respectively. First, based on the ψ-type stability and ψ-type function, the concept of GDS is generalized to include general robust decay synchronization (GRDS) and GDHS. Then, by exploiting a nonlinear controller and different types of inequality techniques, some verifiably sufficient conditions ensuring the GDS and GDHS of SDCDRDNNs (without and with uncertain parameters) are derived. Finally, two simulative examples are provided to demonstrate the validity of the synchronization results obtained.

Finite-time synchronization of memristor neural networks via interval matrix method

In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.

Spacial sampled-data control for H∞ output synchronization of directed coupled reaction-diffusion neural networks with mixed delays

This work investigates the H_∞ output synchronization (HOS) of the directed coupled reaction-diffusion (R-D) neural networks (NNs) with mixed delays. Firstly, a model of the directed state coupled R-D NNs is introduced, which not only contains some discrete and distributed time delays, but also obeys a mixed Dirichlet-Neumann boundary condition. Secondly, a spacial sampled-data controller is proposed to achieve the HOS of the considered networks. This type of controller can reduce the update rate in the process of control by measuring the state of networks at some fixed sampling points in the space region. Moreover, some criteria for the HOS are established by designing an appropriate Lyapunov functional, and some quantitative relations between diffusion coefficients, mixed delays, coupling strength and control parameters are given accurately by these criteria. Thirdly, the case of directed spatial diffusion coupled networks is also studied and, the following finding is obtained: the spatial diffusion coupling can suppress the HOS while the state coupling can promote it. Finally, one example is simulated as the verification of the theoretical results.

Finite-time nonfragile time-varying proportional retarded synchronization for Markovian Inertial Memristive NNs with reaction-diffusion items

The issue of synchronization for a class of inertial memristive neural networks over a finite-time interval is investigated in this paper. Specifically, reaction-diffusion items and Markovian jump parameters are both considered in the system model, meanwhile, a novel nonfragile time-varying proportional retarded control strategy is proposed. First, a befitting variable substitution is invoked to transform the original second-order differential system into a first-order one so that the corresponding synchronization error system that is represented by a first-order differential form is established. Second, by utilizing the integral inequality technique, reciprocally convex combination approach and free-weighting matrix method, a less conservative synchronization criterion in terms of linear matrix inequalities is obtained. Finally, three simulations are exploited to illustrate the feasibility, practicability and superiority of the designed controller so that the acquired theoretical results are supported.

Distributed Optimization of Multiagent Systems With Preserved Network Connectivity

This paper deals with the problem of distributed optimization of a multiagent system with network connectivity preservation. In order to realize cooperative interactions, a connected network is the prerequisite for high-quality information exchange among agents. However, sensing or communication capability is range-limited, so it is impractical to simply make an assumption that network connectivity is preserved by default. To address this concern, a class of generalized potentials including discontinuities caused by unexpected obstacles or noises are designed. For a class of quadratic cost functions, based on the potentials, a new distributed protocol is proposed to formally guarantee the network connectivity over time and to realize the state agreement in finite time while the sum of local functions known to individual agents is optimized. Since the right-hand side of the proposed protocol is discontinuous, some nonsmooth analysis tools are applied to analyze system performance. In some practical scenarios, where initial states are unavailable, a distributed protocol is further developed to realize the consensus in a prescribed finite time while solving the distributed optimization problem and maintaining network connectivity. Illustrative examples are provided to demonstrate the effectiveness of the proposed protocols.

Synchronization of Multiple Reaction-Diffusion Neural Networks With Heterogeneous and Unbounded Time-Varying Delays

The synchronization problem of multiple/coupled reaction-diffusion neural networks with time-varying delays is investigated. Differing from the existing considerations, state delays among distinct neurons and coupling delays among different subnetworks are included in the proposed model, the assumptions posed on the arisen delays are very weak, time-varying, heterogeneous, even unbounded delays are permitted. To overcome the difficulties from this kind of delay as well as diffusion effects, a comparison-based approach is applied to this model and a series of algebraic criteria are successfully obtained to verify the global asymptotical synchronization. By specifying the existing delays, some M -matrix-based criteria are derived to justify the power-rate synchronization and exponential synchronization. In addition, new criterion on synchronization of general connected neural networks without diffusion effects is also given. Finally, two simulation examples are given to verify the effectiveness of the obtained theoretical results and provide a comparison with the existing criterion.

Global Synchronization of Coupled Fractional-Order Recurrent Neural Networks

This paper presents new theoretical results on the global synchronization of coupled fractional-order recurrent neural networks. Under the assumptions that the coupled fractional-order recurrent neural networks are sequentially connected in form of a single spanning tree or multiple spanning trees, two sets of sufficient conditions are derived for ascertaining the global synchronization by using the properties of Mittag-Leffler function and stochastic matrices. Compared with existing works, the results herein are applicable for fractional-order systems, which could be viewed as an extension of integer-order ones. Two numerical examples are presented to illustrate the effectiveness and characteristics of the theoretical results.

Distributed Adaptive Tracking Synchronization for Coupled Reaction-Diffusion Neural Network

This paper considers the tracking synchronization problem for a class of coupled reaction-diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples.

Distributed H∞ State Estimation Over a Filtering Network With Time-Varying and Switching Topology and Partial Information Exchange

This paper is concerned with the distributed H_∞ state estimation for a discrete-time target linear system over a filtering network with time-varying and switching topology and partial information exchange. Both filtering network topology switching and partial information exchange between filters are simultaneously considered in the filter design. The topology under consideration evolves not only over time but also by an event switch which is assumed to be subject to a nonhomogeneous Markov chain. The probability transition matrix of the nonhomogeneous Markov chain is time-varying. In the filter information exchange, partial state estimation information and channel noise are simultaneously considered. In order to design such a switching filtering network with partial information exchange, stochastic Markov stability theory is developed. The switching topology-dependent filters are derived to guarantee an optimal H_∞ disturbance rejection attenuation level for the estimation disagreement of the filtering network. It is shown that the addressed H_∞ state estimation problem is turned into a switching topology-dependent optimal problem. The distributed filtering problem with complete information exchanges from its neighbors is also investigated. An illustrative example is given to show the applicability of the obtained results.

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.