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This paper investigates the event-triggered containment control problem of a class of uncertain nonlinear multiagent systems (MASs). By employing the local relative information, we design an adaptive event-triggered containment algorithm. The proposed containment algorithm can cope with the unavailability of global topology information and uncertain dynamics of follower agents. Therefore, the presented containment algorithm is free of global topology information, i.e., the designed algorithm is fully distributed. In addition, it is proved that Zeno behavior will not occur. At last, a numerical example is given to verify our event-triggered containment algorithm.

During past two decades, cooperative control of MASs has been a hot research field for the reason of broad engineering applications, such as formation control [

MASs can be divided into three cases, i.e., leaderless MASs, leader-follower MASs, and multileader MASs. The control objectives of those three kinds of MASs are consensus control, tracking control, and containment control, respectively. Consensus control and tracking control have been widely studied, from linear MASs [

Cooperative algorithms of MASs use the local information to achieve global control tasks. However, most of the existing control algorithms of MASs need the information of Laplacian which is a global information. Control algorithms that do not need any global information are said to be fully distributed. Many researchers devoted to develop the fully distributed algorithms for MASs. Papers [

Inspired by the above papers, we study the fully distributed event-triggered containment problem of a class of uncertain MASs. Not only the Laplacian of MASs but also the dynamics of follower agents are unavailable to design the containment controllers. To deal with these two unknown data, adaptive techniques are used to design event-triggered containment controllers. The main contributions of this paper are listed as follows: (i) our containment algorithm is fully distributed and does not use any global information of MASs; (ii) our containment algorithm is robust and still works when the dynamics of follower agent is uncertain; and (iii) our presented event-triggered algorithm is free of Zeno behavior.

In this paper, there are

For the topology of MASs, we have the following assumption.

For every follower agent

The induced subgraph of follower agents is an undirected graph.

Since each leader agent is not influenced by other agents, the associated Laplacian matrix can be partitioned as follows:

If Assumptions 1 and 2 hold,

A set

In this paper, we study event-triggered containment control problem of uncertain MASs without using any global topology information.

Consider a network system of

Based on the fact that

Suppose that both

For the control input of each leader, we assume that

The control objective of MASs (

In this section, we will give an adaptive event-triggered algorithm to solve the containment problem of MASs (

Let

From Lemma

Denote

Let

By using

The trigger function for adaptive controller (

Usually, the feedback gain of a consensus controller depends on the eigenvalues of the Laplacian matrix, which are the global topology information. Since adaptive gains

Trigger function (

In the design of dynamical controller (

Denote

Then, combining (

Suppose that Assumptions 1 and 2 hold, containment problem of MASs (

Take Lyapunov function candidate as

Along with (

From the definition of

Hence, we get

Denote

For the third term of

Note that

For the fourth, fifth, and sixth terms, one obtains

Hence, we have

Substituting (

Note that

Combining (

Choosing enough large

Then, Riccati equation (

Since

Combining (

After simple calculations, we have

In the last step, we prove that event-triggered controller (

When

Since

Denote

And, one gets

Notice that

Let

Because

By (

Due to the existence of positive real

One numerical example is given in this section to verify the adaptive event-triggered containment controller (

Consider a leader-follower multiagent system with four follower agents and two leader agents. The Laplacian matrix associated with topology is given as follows:

The dynamics of leaders is depicted by the linearized model of the longitudinal dynamics of an aircraft [

We set the initial values of adaptive gains

The simulation results are presented in Figures

Triggering instants of each follower agent.

Adaptive gains

Norms of

In this paper, we have studied the event-triggered containment problem of a class of uncertain MASs. The global topology information is unavailable, and parameters of follower agents are uncertain. Based on adaptive control technique, we have proposed an event-triggered containment controller which does not rely on any global topology information and can estimate the uncertain parameters. Under this containment algorithm, follower agents enter into the convex hull of leader agents. Moreover, the proposed algorithm has no Zeno behavior. In the future, we will concentrate our study on event-triggered consensus problem of MAS with unknown control directions.

The simulation data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China under Grant nos. 61803193, 61803194, and 61773193, the Postdoctoral Scientific Foundation of China under Grant 2017M620183, and Jiangsu Planned Projects for Postdoctoral Research Funds under Grant 1701077B.