Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control

Adaptive Intermittent Pinning Control for Synchronization of Delayed Nonlinear Memristive Neural Networks With Reaction-Diffusion Items

In this article, the global exponential synchronization problem is investigated for a class of delayed nonlinear memristive neural networks (MNNs) with reaction-diffusion items. First, using the Green formula, Lyapunov theory, and proposing a new fuzzy adaptive pinning control scheme, some novel algebraic criteria are obtained to ensure the exponential synchronization of the concerned networks. Furthermore, the corresponding control gains can be promptly adjusted based on the current states of partial nodes of the networks. Besides, a fuzzy adaptive aperiodically intermittent pinning control law is also designed to synchronize the fuzzy MNNs (FMNNs). The controller with intermittent mechanism can obtain appropriate rest time and save energy consumption. Finally, some numerical examples are provided to confirm the effectiveness of the results in this article.

Input-to-state stabilization of discrete-time delayed fuzzy systems via aperiodically intermittent control

This paper studies input-to-state stabilization of delayed discrete-time Takagi-Sugeno (T-S) fuzzy systems via aperiodically intermittent control. We first consider aperiodically intermittent time-triggered control, where we present sufficient conditions via the mathematical induction under the hypotheses of the quasiperiodicity condition. Based on the derived sufficient conditions, we apply a Lyapunov-Krasovskii (L-K) method together with the descriptor method to derive the explicit linear matrix inequalities (LMIs) that ensure the exponential stability and input-to-state stability (ISS), and show the existence of the aperiodically intermittent time-triggered controller that leads to efficient results with much less numerical complexity. We next consider aperiodically intermittent dynamic event-triggered control with an additional parameter that is larger than one. This strategy allows that the introduced dynamical variable does not remain constant but increases during the control rest interval. As a result, the proposed dynamic event-triggered strategy leads to a smaller number of sent signals than that for the case of the additional parameter which equals to one. Finally, numerical examples including a practical inverted pendulum on a cart are presented to verify the validity of the proposed method.

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.

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.

Bipartite synchronization of Lur'e network with signed graphs based on intermittent control

In this paper, the bipartite synchronization of signed Lur'e network is studied under intermittent control, where the communication relationship of these adjacent nodes in the network can be either cooperative or competitive. Assuming that the network is structurally balanced, bipartite synchronization can be reached with some conditions and coordinate transform criterion. Then, Based on Lyapunov stability theory, some important norms are established. Ultimately, the simulation results can illustrate validness of theoretical analysis.

Stabilization of Discrete-Time Stochastic Delayed Neural Networks by Intermittent Control

This article investigates the stabilization of discrete-time stochastic neural networks with time-varying delay via aperiodically intermittent control (AIC). A comprehensive analysis of the stabilization of discrete-time delayed systems via AIC is provided, where the Lyapunov function method and the Lyapunov-Krasovskii functional method are investigated, respectively. Then, three stabilization criteria are given, which extend previous works from the continuous-time framework to the discrete-time one, and the average activation time ratio (AATR) of AIC is estimated. It is highlighted that for the Lyapunov-Krasovskii functional method, a more flexible estimation for the AATR can be obtained. Finally, the differences and the advantages of the three stabilization criteria are illustrated by numerical simulations.

Aperiodically intermittent saturation consensus on multi-agent systems with discontinuous dynamics

This paper mainly investigates the exponential consensus problem for the multi-agent systems (MASs) with nonlinear discontinuous dynamics and time-varying delay. A novel aperiodically intermittent distributed control strategy is proposed to force the state of each agent to the common trajectory, where the configuration of control width and rest width can be aperiodic. Meanwhile, in order to limit the control effects into certain reasonable ranges, an improved saturation algorithm is proposed, which effectively reduces the non-smoothness of the control signal. Sufficient conditions for the exponential consensus on the discontinuous MASs are obtained through the Filippov differential inclusion (FDI), the Lie derivative method (LDM) and the measurement selection theorem (MST). Finally, the validity and feasibility of the main theories is demonstrated by numerical simulations.

New Criteria for Synchronization of Multilayer Neural Networks via Aperiodically Intermittent Control

In this paper, the globally asymptotic synchronization of multi-layer neural networks is studied via aperiodically intermittent control. Due to the property of intermittent control, it is very hard to deal with the effect of time-varying delays and ascertain the control and rest widths for intermittent control. A new lemma with generalized Halanay-type inequalities are proposed first. Then, by constructing a new Lyapunov–Krasovskii functional and utilizing linear programming methods, several useful criteria are derived to ensure the multilayer neural networks achieve asymptotic synchronization. Moreover, an aperiodically intermittent control is designed, which has no direct relationship with control widths and rest widths and extends existing aperiodically intermittent control techniques, the control gains are designed by solving the linear programming. Finally, a numerical example is provided to confirm the effectiveness of the proposed theoretical results.

Stability of Time-Varying Hybrid Stochastic Delayed Systems With Application to Aperiodically Intermittent Stabilization

This article is concerned with the stability analysis of time-varying hybrid stochastic delayed systems (HSDSs), also known as stochastic delayed systems with Markovian switching. Several easy-to-check and less conservative Lyapunov-based sufficient criteria are derived for ensuring the stability of studied systems, where the upper bound estimation for the diffusion operator of the Lyapunov function is time-varying, piecewise continuous, and indefinite. It should be stressed that our results can be directly used to analyze the stabilization of HSDSs via aperiodically intermittent control (AIC). Compared with the existing results about AIC, the restrictions on the bound of each control/rest width and the maximum proportion of rest width in each control period are removed. Thus, the conservativeness is reduced. Finally, two examples, together with their numerical simulations, are provided to demonstrate the theoretical results.

Prefixed-Time Local Intermittent Sampling Synchronization of Stochastic Multicoupling Delay Reaction-Diffusion Dynamic Networks

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.

Synchronization Control for Discrete-Time-Delayed Dynamical Networks With Switching Topology Under Actuator Saturations

This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the l₂ - l_∞ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the l₂ - l_∞ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.

Master-Slave Synchronization of Delayed Neural Networks With Time-Varying Control

This brief investigates the master-slave synchronization problem of delayed neural networks with general time-varying control. Assuming a linear feedback controller with time-varying control gain, the synchronization problem is recast into the stability problem of a delayed system with a time-varying coefficient. The main theorem is established in terms of the time average of the control gain by using the Lyapunov-Razumikhin theorem. Moreover, the proposed framework encompasses some general intermittent control schemes, such as the switched control gain with external disturbance and intermittent control with pulse-modulated gain function, while some useful corollaries are consequently deduced. Interestingly, our theorem also provides a solution for regaining stability under control failure. The validity of the theorem and corollaries is further demonstrated with numerical examples.

Impulsive Synchronization of Unbounded Delayed Inertial Neural Networks With Actuator Saturation and Sampled-Data Control and its Application to Image Encryption

The article considers the impulsive synchronization for inertial neural networks with unbounded delay and actuator saturation via sampled-data control. Based on an impulsive differential inequality, the difficulties caused by unbounded delay and impulsive effect may be effectively avoid. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequality (LMI) criteria that guarantee asymptotical synchronization for the considered model via hybrid control are given. As special cases, the asymptotical synchronization of the considered model via sampled-data control and saturating impulsive control are also studied, respectively. Numerical simulations are presented to claim the effectiveness of theoretical analysis. A new image encryption algorithm is proposed to utilize the synchronization theory of hybrid control. The validity of image encryption algorithm can be obtained by experiments.

Exponential quasi-synchronization of coupled delayed memristive neural networks via intermittent event-triggered control

Firstly, an intermittent event-triggered control (IETC), as a combination of intermittent control and event-triggered control, is proposed. Then, the quasi-synchronization problem of coupled memristive neural networks with time-varying delays (CDMNN) is discussed under this IETC. To include more of the existing work, aperiodic intermittent control and event-triggered control with combined measurement errors are adopted in the IETC. Under the IETC, it is shown that Zeno behavior cannot be exhibited for CDMNN. At the same time, two new differential inequalities are established, and some simple and practical criteria for CDMNN quasi-synchronization and synchronization are obtained by using these inequalities. In the obtained results, synchronization is a spatial case of quasi-synchronization, and the activation functions of DMNN do not need to be bounded. Finally, a numerical example and some simulations are provided to test the results in theoretical analysis.

Aperiodically intermittent control for exponential bipartite synchronization of delayed signed networks with multi-links

This paper investigates the exponential bipartite synchronization of a general class of delayed signed networks with multi-links by using an aperiodically intermittent control strategy. The main result is a set of sufficient conditions for bipartite synchronization that depend on the network's topology, control gain, and the maximum proportion of rest time. An application to Chua's circuits is then considered, and some numerical simulation results are presented.

Quasi-Synchronization of Delayed Memristive Neural Networks via Region-Partitioning-Dependent Intermittent Control

This paper aims at investigating the master-slave quasi-synchronization of delayed memristive neural networks (MNNs) by proposing a region-partitioning-dependent intermittent control. The proposed method is described by three partitions of non-negative real region and an auxiliary positive definite function. Whether the control input is imposed on the slave system or not is decided by the dynamical relationships among the three subregions and the auxiliary function. From these ingredients, several succinct criteria with the associated co-design procedure are presented such that the synchronization error converges to a predetermined level. The proposed intermittent control scheme is also applied to the event-triggered control, and an intermittent event-triggered mechanism is devised to investigate the quasi-synchronization of MNNs correspondingly. Such mechanism eliminates the events in rest time, and then it reduces the amount of samplings. Finally, two illustrative examples are presented to verify the effectiveness of our theoretical results.

Stability of Singular Discrete-Time Neural Networks With State-Dependent Coefficients and Run-to-Run Control Strategies

In this brief, sustaining and intermittent run-to-run controllers are designed to achieve the stability of singular discrete-time neural networks with state-dependent coefficients. The controllers are designed for two reasons: 1) it is very difficult and almost impossible to only measure the in situ feedback information for the controllers and 2) the controllers may not always exist at any time. The stability is then established for singular discrete-time neural networks with state-dependent coefficients. Finally, numerical simulations are shown to illustrate the usefulness of the obtained criteria.

Cluster Synchronization for Interacting Clusters of Nonidentical Nodes via Intermittent Pinning Control

The cluster synchronization problem is investigated using intermittent pinning control for the interacting clusters of nonidentical nodes that may represent either general linear systems or nonlinear oscillators. These nodes communicate over general network topology, and the nodes from different clusters are governed by different self-dynamics. A unified convergence analysis is provided to analyze the synchronization via intermittent pinning controllers. It is observed that the nodes in different clusters synchronize to the given patterns if a directed spanning tree exists in the underlying topology of every extended cluster (which consists of the original cluster of nodes as well as their pinning node) and one algebraic condition holds. Structural conditions are then derived to guarantee such an algebraic condition. That is: 1) if the intracluster couplings are with sufficiently strong strength and the pinning controller is with sufficiently long execution time in every period, then the algebraic condition for general linear systems is warranted and 2) if every cluster is with the sufficiently strong intracluster coupling strength, then the pinning controller for nonlinear oscillators can have its execution time to be arbitrarily short. The lower bounds are explicitly derived both for these coupling strengths and the execution time of the pinning controller in every period. In addition, in regard to the above-mentioned structural conditions for nonlinear systems, an adaptive law is further introduced to adapt the intracluster coupling strength, such that the cluster synchronization for nonlinear systems is achieved.

Synchronization of coupled stochastic complex-valued dynamical networks with time-varying delays via aperiodically intermittent adaptive control

This paper deals with the synchronization problem of a class of coupled stochastic complex-valued drive-response networks with time-varying delays via aperiodically intermittent adaptive control. Different from the previous works, the intermittent control is aperiodic and adaptive, and the restrictions on the control width and time delay are removed, which lead to a larger application scope for this control strategy. Then, based on the Lyapunov method and Kirchhoff's Matrix Tree Theorem as well as differential inequality techniques, several novel synchronization conditions are derived for the considered model. Specially, impulsive control is also considered, which can be seen as a special case of the aperiodically intermittent control when the control width tends to zero. And the corresponding synchronization criteria are given as well. As an application of the theoretical results, a class of stochastic complex-valued coupled oscillators with time-varying delays is studied, and the numerical simulations are also given to demonstrate the effectiveness of the control strategies.

Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control

In this paper, the finite-time and fixed-time cluster synchronization problem for complex networks with or without pinning control are discussed. Finite-time (or fixed-time) synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time, and the settling time depends on the initial values for finite-time synchronization (or the settling time is bounded by a constant for any initial values for fixed-time synchronization). To realize the finite-time and fixed-time cluster synchronization, some simple distributed protocols with or without pinning control are designed and the effectiveness is rigorously proved. Several sufficient criteria are also obtained to clarify the effects of coupling terms for finite-time and fixed-time cluster synchronization. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.

Synchronization of Hierarchical Time-Varying Neural Networks Based on Asynchronous and Intermittent Sampled-Data Control

In this brief, our purpose is to apply asynchronous and intermittent sampled-data control methods to achieve the synchronization of hierarchical time-varying neural networks. The asynchronous and intermittent sampled-data controllers are proposed for two reasons: 1) the controllers may not transmit the control information simultaneously and 2) the controllers cannot always exist at any time . The synchronization is then discussed for a kind of hierarchical time-varying neural networks based on the asynchronous and intermittent sampled-data controllers. Finally, the simulation results are given to illustrate the usefulness of the developed criteria.In this brief, our purpose is to apply asynchronous and intermittent sampled-data control methods to achieve the synchronization of hierarchical time-varying neural networks. The asynchronous and intermittent sampled-data controllers are proposed for two reasons: 1) the controllers may not transmit the control information simultaneously and 2) the controllers cannot always exist at any time . The synchronization is then discussed for a kind of hierarchical time-varying neural networks based on the asynchronous and intermittent sampled-data controllers. Finally, the simulation results are given to illustrate the usefulness of the developed criteria.

Pinning Impulsive Synchronization of Reaction-Diffusion Neural Networks With Time-Varying Delays

This paper investigates the exponential synchronization of reaction-diffusion neural networks with time-varying delays subject to Dirichlet boundary conditions. A novel type of pinning impulsive controllers is proposed to synchronize the reaction-diffusion neural networks with time-varying delays. By applying the Lyapunov functional method, sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction-diffusion neural networks with large and small delay sizes. It is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network; the technique used in this paper is also applicable to reaction-diffusion networks with Neumann boundary conditions. Numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction-diffusion terms via aperiodically intermittent control

In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.