Outer synchronization of complex networks with internal delay and coupling delay via aperiodically intermittent pinning control

Nonperiodic intermittent control for pinning synchronization of directed dynamical networks with internal delay and hybrid coupling

This paper focuses on the synchronization for the delayed bipartite networks with non-delay and delay couplings. Different from single networks, the nodes of bipartite networks can be divided into two disjoint nonempty sets according to their properties or dynamics characteristics, and the nodes in different sets can be connected by edges while the nodes in the same set cannot be connected. In this bipartite network model, the node and coupling delays are simultaneously considered, and both the non-delay and delay coupling matrices are undirected and weighed. Furthermore, the intermittent control method used in this paper can be aperiodic while in most previous works are periodic. Based on the Lyapunov function method, block multiplication of matrices and other mathematical techniques, several synchronization protocols are rigorously induced. Finally, the proposed control method is evaluated by utilizing numerical simulation.

This paper considers finite-time synchronization of complex multi-links dynamical networks with or without internal time delays via intermittent controls. Two simple intermittent feedback controllers are designed to achieve finite-time synchronization between the drive and response system. Some novel and effective finite-time synchronization criteria are derived based on finite-time stability analysis techniques. By constructing suitable Lyapunov functions, we theoretically prove its correctness. Finally, two numerical simulation examples are given to show the effectiveness of proposed method in this paper.

Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance

This paper is concerned with the finite-time synchronization problem of coupled drive-response systems with time-varying delays via quantized adaptive aperiodically intermittent control. Compared with previous research results, the intermittent control is aperiodic and coupling functions are nonlinear. Furthermore, both internal time-varying delays and coupling time-varying delays are considered. By employing Lyapunov–Krasovskii functional method and Kirchhoff’s Matrix Tree Theorem, some novel sufficient conditions are derived to guarantee that drive-response systems can achieve synchronization in finite time. Specially, the convergence time is discussed. It is worth pointing out that the convergence time is closely related to topological structure of networks and the maximum ratio of the rest width to the aperiodical time span. Finally, finite-time synchronization of a typical second-order Kuramoto model with time-varying delays and Chua’s circuits model with time-varying delays are studied by using our theoretical results. Meanwhile, the numerical simulations are given to illustrate the effectiveness of the theoretical results we obtained.

Outer synchronization between the drive network and the response network has attracted much more attention in various fields of science and engineering. In this paper, mixed outer synchronization between two complex dynamical networks with nonidentical nodes and output coupling is investigated via impulsive hybrid control, that is, an adaptive feedback controller with impulsive control effects. Moreover, both the cases of complex networks without and with coupling delay are considered. According to the stability analysis of the impulsive functional differential equation, several sufficient conditions for the networks to achieve mixed outer synchronization are derived. Numerical examples are presented finally to illustrate the effectiveness and advantage of the proposed synchronization criteria.

Synchronization of multi-weighted complex networks with mixed variable delays and uncertainties via impulsive pinning control

In this paper, the exponential stability is studied for a class of coupled neural networks, in which the model has nodes of different dimensions, and has different internal time-delays and coupling delays. Based on Lyapunov stability theory and linear matrix inequality technique, some sufficient conditions are derived for ensuring the exponential stability of the equilibrium of system. Finally, a numerical example is given to show the effectiveness of our results.

Synchronization of stochastic complex networks with discrete-time and distributed coupling delayed via hybrid nonlinear and impulsive control

This paper studies the outer synchronization problem of discrete fractional complex networks (DFCNs) with and without the presence of unknown topology. A discrete complex network with a fractional difference is first established and analyzed. By constructing a suitable Lyapunov function and utilizing properties of the fractional difference, outer synchronization criteria for the DFCNs with and without unknown topology are established based on linear matrix inequalities. Meanwhile, the unknown parameters in the topology structure of the network can be identified by adaptive update laws. In the end, two numerical examples are given to exemplify the validity and applicability of the obtained results.

Finite-time synchronization of multi-layer nonlinear coupled complex networks via intermittent feedback control

A periodic intermittent adaptive control method with saturation is proposed to pin the quasi-consensus of nonlinear heterogeneous multi-agent systems with external disturbances in this paper. A new periodic intermittent adaptive control protocol with saturation is designed to control the internal coupling between the follower agents and the feedback gain between the leader and the follower. In particular, we use the saturation adaptive law: when the quasi-consensus error converges to a certain range, the adaptive coupling edge weight and the adaptive feedback gain will not be updated. Furthermore, we propose three saturated adaptive pinning control protocols. The quasi-consensus is achieved through its own pinning as long as the agents remain connected to each other. Using the Lyapunov function method and inequality technique, the convergence range of the quasi-consensus error of a heterogeneous multi-agent system is obtained. Finally, the rationality of the proposed control protocol is verified through numerical simulation. Theoretical derivation and simulation results show that the novel proposed periodic intermittent adaptive control method with saturation can successfully be used to achieve the pinning of quasi-consensus of nonlinear heterogeneous multi-agent systems.

The synchronization in complex network model with time-delay nodes is investigated. The model is applicable for two sorts of complex networks. With linear feedback controller and adaptive feedback controller, positive definite functions are designed respectively. The sufficient conditions of synchronization are given by Lyapunov stability theory. Finally, numerical simulations show the effectiveness of the synchronization in complex networks.

On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays

This paper is devoted to the study of synchronization problems in uncertain dynamical networks with time-delayed nodes and coupling delays. First, a complex dynamical network model with time-delayed nodes and coupling delays is given. Second, for a complex dynamical network with known or unknown but bounded nonlinear couplings, an adaptive controller is designed, which can ensure that the state of a dynamical network asymptotically synchronizes at the individual node state locally or globally in an arbitrary specified network. Then, the Lyapunov-Krasovskii stability theory is employed to estimate the network coupling parameters. The main results provide sufficient conditions for synchronization under local or global circumstances, respectively. Finally, two typical examples are given, using the M-G system as the nodes of the ring dynamical network and second-order nodes in the dynamical network with time-varying communication delays and switching communication topologies, which illustrate the effectiveness of the proposed controller design methods.