Pinning Control Strategy Research Articles

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.

Synchronization of fractional-order dynamical network via aperiodically intermittent pinning control

In this paper, synchronization of fractional-order network is investigated. The aperiodically intermittent pinning control scheme is adopted to design effective controllers for achieving the synchronization. Noticeably, the topology is directed and only the first node is controlled. Based on the Lyapunov function method and mathematical analysis technique, some sufficient conditions are derived and demonstrated to be effective by a numerical example.

Nonperiodically intermittent pinning synchronization of complex-valued complex networks with non-derivative and derivative coupling

Considering the fact that time delays in practical systems are unavoidable and cannot be ignored, this paper studies nonperiodically intermittent pinning synchronization of delayed complex-valued complex dynamical networks with derivative coupling and parameters perturbation, in which the considered node systems have bounded parametric uncertainties. Different from previous works, the time-varying delays exist in the complex-valued node dynamics and non-derivative coupling forms. A nonperiodically intermittent pinning control scheme is proposed to stabilize the error system of drive–response complex-valued dynamical networks. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, firstly, the sufficient condition is derived, where the free time delay is considered; secondly, the synchronization condition is obtained, where we take into account the constrained time delay. Finally, numerical examples are given to illustrate the correctness of the obtained results and the theoretical analysis.

Global pinning synchronization of stochastic delayed complex networks

In this paper, the global pinning synchronization problem of a class of complex dynamical networks with hybrid couplings, time delays, random data packet dropouts and multiple stochastic disturbances is investigated. The hybrid couplings are portrayed in three forms: constant couplings, discrete-delay couplings and distributed-delay couplings. The phenomenon of random packet dropouts is described as a binary random variable which obeys the Bernoulli distribution taking values of 0 and 1 with a certain probability. Multiple noisy processes herein are characterized by Brownian motions, which act on all coupling terms as well as the overall dynamics equation. By applying the Lyapunov method and stochastic analysis technique, sufficient conditions are established to ensure the considered stochastic delayed complex network to globally synchronize to a reference trajectory in the mean-square sense via the developed randomly occurring pinning control strategy. The obtained criteria are within the framework of linear matrix inequations. Finally, a simulation example is presented to verify the feasibility and effectiveness of the derived theoretical results.

Dynamic event-triggered approach for cluster synchronization of complex dynamical networks with switching via pinning control

This paper focuses on the cluster synchronization problem for complex dynamical networks with switching signal which is characterized by average dwell-time constraint. To reduce networks burden, a dynamic event-triggered mechanism and pinning control strategy is firstly introduced to the design of cluster synchronization controllers for a class of switched complex networks. By constructing piecewise continuous Lyapunov functions and utilizing stability analysis methods, the cluster synchronization conditions are proposed under which the synchronization error dynamics with the dynamic event-triggered rule is stable. Finally, one numerical example is presented to show the effectiveness of the theoretical results.

Cluster synchronization in a complex dynamical network of non-identical nodes with delayed and non-delayed coupling via pinning control

Synchronization of complex dynamical networks has been a hot topic for its practical applications. In this paper, the cluster synchronization of a complex dynamical network via pinning control is investigated. The nodes in different clusters are assumed to be non-identical. The network topology is assumed to be directed and non-symmetric. Both the non-delayed and delayed coupling are considered to be more realistic. Based on the Lyapunov stability theory, a simple and useful pinning control scheme is derived. Furthermore, numerical simulations show that our control strategy is quite effective and convenient.

Robust Exponential Synchronization for Memristor Neural Networks With Nonidentical Characteristics by Pinning Control

In this paper, robust exponential synchronization of memristor-based neural networks (MNNs) with nonidentical characteristics is investigated. Coefficient mismatch, time-varying delay mismatch, and activation function mismatch are considered between the drive and the response MNNs. Pinning control strategy is developed to realize robust exponential synchronization and the stability criteria is established by using the Lyapunov function method and differential inclusion theory. Furthermore, the stable region of controller parameters is computed to guarantee that the synchronization errors enter a predetermined error bound within given settling time. Finally, the effectiveness of the proposed methods is verified by the numerical simulations. The methods presented in this paper offer novel schemes for robust exponential synchronization of nonidentical MNNs.

Out Lag Synchronization of Fractional Order Delayed Complex Networks with Coupling Delay via Pinning Control

This paper discusses the out lag synchronization of fractional order complex networks (FOCN) including both internal delay and coupling delay and with the employment of pinning control scheme. Using comparison theorem and constructing the auxiliary function, several synchronization criterions by linear feedback pinning control are presented. The model and the obtained results in this work are more general than the previous works. Correctness and effectiveness of the theoretical results are validated through numerical simulations.

Cluster synchronization of fractional-order directed networks via intermittent pinning control

In this paper, cluster synchronization of fractional-order directed network is investigated. The intermittent pinning control scheme is adopted to design effective controllers for achieving the cluster synchronization. Only the first node in each cluster needs to be controlled. Based on the Lyapunov function method and mathematical analysis technique, some sufficient conditions of cluster synchronization in the given network are derived and demonstrated to be effective by diverse numerical examples.

Event-Based Time-Interval Pinning Control for Complex Networks on Time Scales and Applications

This paper studies the synchronization problem for linear complex dynamical networks (CDNs) on time scales. An intermittent dynamic time-interval pinning control strategy is designed to achieve synchronization for CDNs with the isolated node. Based on the Lyapunov approach and the theory of time scales, synchronization criteria are established for CDNs on general time scales. The main results in the paper show that, by controlling a proportion of the network nodes, the exponential synchronization can be achieved. Moreover, the infinitely fast switching of the pinning node set is avoided by means of the event-triggered strategy. According to our selection algorithm, the number of pinning nodes will be updated online at each pinning time. The modeling framework investigated in this paper is a unification and generalization of many existing continuous-time and discrete-time complex network models. Three numerical examples are given to illustrate the effectiveness and priority of the obtained results. Finally, the analytical results are applied to the distributed auxiliary control of microgrids and formation control of spacecraft.

Controllability of complex networks: Choosing the best driver set

Identifying the best driver set in a complex network is an unsolved problem in the application of pinning control methods. We choose the eigenratio of the augmented Laplacian matrix, and the best driver set is the subset of nodes providing the most effective pinning control strategy, i.e. the one for which synchronization of the whole network to the reference state is attained over the widest range of the coupling parameter. In this work, we propose a centrality measure based on sensitivity analysis of the Laplacian matrix of the connection graph to find an approximate solution to this problem. The proposed metric is computationally efficient as it requires only a single eigen-decomposition of the Laplacian matrix. Numerical results on a number of sample networks show that the proposed metric has significantly better accuracy than currently used heuristics, and in most cases can correctly identify the true optimal set, which is obtainable through combinatorial search.

Outer synchronization of a class of mixed delayed complex networks based on pinning control

In this paper, the problem on outer synchronization is investigated for a class of mixed delayed complex networks by using the pinning control strategy. Together with some Lyapunov–Krasovskii functional and effective mathematical techniques, several conditions are derived to guarantee a class of complex networks with mixed delays to be outer synchronization. By proposing a novel functional condition which has not been proposed so far, further improved synchronization criteria are proposed. Finally, two examples are given to illustrate the effectiveness of the results.

Fractional PI pinning synchronization of fractional complex dynamical networks

A novel method for synchronization of fractional order complex dynamical networks using a new fractional Proportional–Integral (PI) pinning control scheme is presented in this paper. Stability of this network is proved via the Lyapunov stability theorem, and the synchronizability criterion is obtained. Although one can also design a proportional pinning control scheme to synchronize the whole network, our proposed fractional PI control is more efficient. Numerical simulations on Lorenz oscillator’s interaction over a sample network have shown that the proposed fractional PI controller can provide a faster synchronization with less overshoot to the reference state compared to conventional proportional controller with the same power consumption.

Bipartite synchronization in coupled delayed neural networks under pinning control

This paper considers the bipartite leader-following synchronization in a signed network composed by an array of coupled delayed neural networks by utilizing the pinning control strategy and M-matrix theory, where the communication links between neighboring nodes of the network can be either positive or negative. Under the assumption that the node-delay is bounded and differentiable, a sufficient condition in terms of a low-dimensional linear matrix inequality is derived for reaching bipartite leader-following synchronization in the signed network, based on which a simple algebraic formula is further given to estimate an upper bound of the node-delay. When the node-delay is bounded and non-differentiable, some criteria are established by using the descriptor method and the reciprocally convex approach such that the bipartite leader-following synchronization problem for the signed network can be successfully solved. Finally, numerical simulations are provided to illustrate the effectiveness of theoretical analysis.

Cluster synchronization in uncertain network with nonidentical nodes based on adaptive pinning control

We investigate the cluster synchronization in uncertain network with nonidentical nodes based on adaptive pinning control. In this synchronization technology, the network can be arbitrarily divided into several clusters. And the network parameters can be uncertain and they follow a kind of the identification law. By utilizing pinning control strategy, cluster synchronization criterion for the uncertain network has been established. Finally, the numerical simulation is provided to prove the effectiveness of proposed pinning control strategy.

Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes

This paper investigates the quasi-synchronization problem in heterogeneous fractional order dynamic networks with time-delay. Based on comparison theorem for the fractional order differential equation, a new fractional order functional differential inequality is built at first. According to the inequality, some quasi-synchronization conditions are derived via Lyapunov method, and the error bound is estimated. Then, the pinning control strategy is also considered via matrix analysis. Furthermore, the specific pinning schemes about how many nodes are needed to be selected are provided in an algorithm. Finally, two examples are given to verify the validity of our theoretical results.

Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers

In this paper, the globally exponential synchronization problem of dynamical networks with nonlinearly coupling function is considered. Hybrid pinning control strategies are established to force the states of the network to follow some objective trajectory. The impulsive pinning controllers are used to control a fringe of nodes at the impulsive instants, while during the impulsive instants, pinning state-feedback controllers are designed to achieve the control objective. Finally, the validity of the developed techniques is evidenced by an illustrative example.

Cluster lag synchronization of delayed heterogeneous complex dynamical networks via intermittent pinning control

This paper investigates the problem of cluster lag synchronization in the heterogeneous dynamical networks by using an intermittent pinning control strategy. Previous related works mainly focused on the time-varying delays in the self-dynamics, which was not consistent with the real world. The transmission delay in the communication channels is considered in this paper. We present several criteria to guarantee cluster lag synchronization without assuming the coupling matrix being symmetric and irreducible. A decentralized adaptive intermittent pinning control scheme is employed to reduce the control cost. An effective pinned-cluster selection scheme is adopted to guide what kind of clusters should be pinned preferentially. Two simulations are proposed to verify the correctness of the theoretical results.

Synchronization of coupled neural networks with infinite-time distributed delays via quantized intermittent pinning control

How to deal with the effect of infinite-time delay and maximize rest width is the main difficulty for intermittent control techniques. This paper considers asymptotic synchronization of coupled neural networks (CNNs) with bounded time-varying discrete delay and infinite-time distributed delay (mixed delays). A quantized intermittent pinning control scheme is designed to save both channel resources and control cost and reduce both the amount of transmitted information and channel blocking. Two weighted integral inequalities are first established to deal with the infinite-time distributed delay. Based on weighted double-integral inequalities, novel Lyapunov–Krasovskii functionals with negative terms are designed, which can reduce the conservativeness of the results. Some sufficient conditions in the form of linear matrix inequalities are obtained to ensure that the CNNs asymptotically synchronize to an isolated system. Moreover, the relationships between the control width, rest width, and convergence rate are explicitly given. Furthermore, an optimal algorithm is provided to increase the rest width as large as possible. As special cases, the synchronization of the CNNs with quantized pinning control and quantized intermittent control are also considered, respectively. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Pinning Consensus Analysis for Nonlinear Second‐Order Multi‐Agent Systems with Time‐Varying Delays

AbstractThis paper considers the second‐order leader‐following consensus problem for adelayed multi‐agent systems under general network topologies, in which each agent is a time‐delayed second‐order system with inherent nonlinear dynamics. Based on the pinning control strategy, a distributed control algorithm is proposed to achieve the second‐order leader‐following consensus of multi‐agent systems. Using matrix theory, algebraic graph theory and the free‐weighting‐matrix approach, some sufficient conditions are established in terms of linear matrix inequalities to ensure that all the agents can asymptotically follow the virtual leader. Finally, the effectiveness and the advantages of the developed approach are illustrated by means of simulations.