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The exponential synchronization problem is investigated for a class of moving agent networks in a two-dimensional space and exhibits time-varying topology structure. Based on the Lyapunov stability theory, adaptive feedback controllers are developed to guarantee the exponential synchronization between each agent node. New criteria are proposed for verifying the locally and globally exponential synchronization of moving agent networks under the constraint of fast switching. In addition, a numerical example, including typical moving agent network with the Rössler system at each agent node, is provided to demonstrate the effectiveness and applicability of the proposed design approach.

Over the past decade years, the analysis of complex systems from the viewpoint of networks has become an important interdisciplinary issue [

The synchronization properties of a complex network are mainly determined by its topological structures connections between nodes. In the current study of complex networks, most of the existing works on synchronization consider static networks, whose topological structures do not change as time evolves [

Inspired by the above discussions, in this paper we investigate the adaptive exponential synchronization problem for a specific time-varying network model. The model arises from the interaction of mobile agents proposed by Frasca et al. [

Although synchronization control of moving agent network has great application potential in a variety of areas, there has been very little existing literature on the exponential synchronization problem. Therefore, we adopt the constraint of fast switching to derive exponent synchronization conditions. By using Lyapunov stability theory, adaptive controllers are designed for synchronization of moving agent network with time-varying topological structures. The adaptive controllers can ensure the states of moving agent network fast synchronization.

The current paper is organized as follows. A general moving agent network model and several mathematical preliminaries are introduced in Section

We consider

Each agent interacts at a given time with only those agents located within a neighborhood of an interaction radius, defined as

In this paper, the control objective is to make the states of network (

We assume that

Next, the rigorous mathematical definition of exponential synchronization for dynamical network (

Let

In this section, we discuss the exponential synchronization of moving agent network (

In order to achieve the objective of synchronization on the manifold (

Then, exponential synchronization problem of the dynamical network (

Linearizing error system (

In the following, we give several useful hypotheses.

Suppose that there exists a nonnegative constant

Generally, Assumption

Suppose there exists a constant

Assumption

Suppose that a coupled network with fixed topology defined by

The proof of Lemma

According to analysis of [

Based on Assumptions

Suppose that Assumptions

Select a Lyapunov function as follows:

Here, according to Lemma

According to (

Therefore, in closed-loop under the controllers (

Since error dynamical system (

Rewrite node dynamics

Suppose that there exists a nonnegative constant

Suppose that Assumptions

since

Similarly, construct Lyapunov function (

Therefore, in closed-loop under the controllers (

In this paper, the coupling scheme of dynamical network (

In this section, one example is given for illustrating the proposed synchronization criteria. Consider a dynamical network consisting of 5 identical Rössler oscillators, where state dynamics of each agent is described by

Each agent node interacts at a given time with only those agents located within a neighborhood of an interaction radius. Here, we let periodic boundary conditions size

The position each agent during the movement.

When two agents interact (let interaction radius

Obviously, one gets

Assume that

Synchronization errors of

Synchronization errors of

Synchronization errors of

Locally and globally adaptive exponential synchronization of moving agent network has been investigated in this paper. The network with decentralized controllers is considered as a large-scale nonlinear system with time-varying topological structure. An adequate Lyapunov function is constructed to deal with the problem of controlled synchronization so as to ensure the closed-loop system stability. Several network synchronization criteria for such network with time-varying topological have been obtained. And a numerical simulation of coupled Rössler system network is given, which demonstrates the effectiveness of the proposed synchronization scheme.

This research was supported in part by the Natural Science Foundation of Hebei under Grant no. F2012501030, Fundamental Research Funds for the Central Universities under Grant no. N100323012 from the Ministry of Education, and the National Natural Science Foundation of China under Grant no. 51105068.