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In this paper, adaptive guaranteed-performance consensus control problems for multiagent systems with an adjustable convergence speed are investigated. A novel adaptive guaranteed-performance consensus protocol is proposed, where the communication weights can be adaptively regulated. By the state space decomposition method and the stability theory, sufficient conditions for guaranteed-performance consensus are obtained and the guaranteed-performance cost is determined. Moreover, the lower bound of the convergence coefficient for multiagent systems is deduced, which is linearly adjustable approximately by changing the adaptive control gain. Finally, simulation examples are introduced to demonstrate theoretical results.

In recent years, by the incentive effects of spacious applications, such as synchronization [

In some practical complex multiagent systems, except for the requirements of achieving consensus, the consensus performance also needs to be taken into consideration. There is a representative example in [

As is well known, the consensus speed was firstly referred by Olfati-Saber in [

In some practical applications, such as movement and communication, each agent in multiagent systems may have limited energy supply. However, a lot of research works about the consensus control for multiagent systems do not take the above-mentioned important factor into consideration. This paper focuses on the guaranteed-performance consensus analysis of multiagent systems, which can deal with the limited energy problem effectively. Furthermore, the convergence speed plays an essential role in the consensus performance of multiagent systems. Although the convergence speed can be adjusted by changing the algebraic connectivity related to the topology structure, it is usually difficult to change the topology structure in practice. This paper finds that the adjustable convergence speed can be obtained by changing the adaptive control gain, which owns great engineering significance.

The current paper studies adaptive guaranteed-performance consensus control for multiagent systems with an adjustable convergence speed. As far as I am concerned, the contribution of this paper is the following threefold: (i) A new adaptive guaranteed-performance consensus protocol for first-order multiagent systems is proposed, and the communication weights among nodes in the system topology can be adaptively adjustable by state errors between each agent and its neighbors. (ii) The multiagent system is decomposed into two subsystems which determine the consensus motion and the disagreement motion, respectively. Sufficient conditions for guaranteed-performance consensus are obtained, and the guaranteed-performance cost is determined at the same time. (iii) The convergence coefficient is defined for multiagent systems under an adaptive consensus protocol, and the lower bound of the convergence coefficient is determined, which is related to the adaptive control gain and the minimum nonzero eigenvalue.

Compared with the existing relevant works about the consensus problem of multiagent systems, this paper has following novelties. Firstly, a novel consensus control strategy is proposed to guarantee the consensus performance of multiagent systems. Note that it corresponds with practical applications, which means that many systems in aviation and aerospace are constrained by limited energy. However, this method is not available in [

The remainder of the paper is organized as follows. Section

This section mainly introduces some basic concepts of the graph theory and presents the problem description.

From the graph theory, one can see that it is meaningful to describe the information interchange of multiagent systems by connected undirected graph

The following adaptive guaranteed-performance control protocol is proposed:

It can be found that if

In view the undirected topology

The definition of the adaptive guaranteed-performance consensus for multiagent system (

Combined with control protocol (

The aim of this paper is to obtain a suitable adaptive control gain and the guaranteed-performance cost, so that multiagent system (

There is no doubt that the research method between the consensus problem of multiagent systems and the synchronization problem of complex networks is the same, which is sufficiently introduced in [

In the following theoretical analysis, sufficient conditions for multiagent system (

Let

According to the definition of orthogonal matrices, one can see that

In the following theorem, sufficient conditions for adaptive guaranteed-performance consensus are obtained, which means that distributed guaranteed-performance consensus design for multiagent system (

Multiagent (

To begin with, we prove

Because of

In the following discussion, the guaranteed-performance cost is determined. Firstly, one can obtain from (

It can be seen from Theorem

For the sake of verifying the assumption that the proposed method can effectively regulate the convergence speed of multiagent system (

For multiagent system (

As a matter of fact, (

In the following, we determine the convergence coefficient of multiagent system (

Then substituting (

The lower bound of the convergence coefficient of multiagent (

As the improvement of the convergence speed can save working time of multiagent systems in practice to some degree, it is significant to investigate how to improve the convergence speed when multiagent systems achieve consensus. Thus, the adjustable convergence speed is deduced, and the lower bound of the convergence coefficient under control protocol (

By comparison, one can see that although changing the value of

In this section, a simulation example is given to demonstrate the effectiveness of theoretical results shown in the previous analysis.

Consider a first-order multiagent system composed of six agents, where the system topology is depicted by the connected undirected graph shown in Figure

System topology.

For adaptive guaranteed-performance control protocol (

Figure

State trajectories under control protocol (

State trajectories under the standard consensus protocol.

Guaranteed-performance function of multiagent system (

The relationship between convergence time and reciprocal of adaptive control gain.

From Theorem

A new adaptive guaranteed-performance consensus scheme for multiagent systems with an adjustable convergence speed was proposed in this paper. The adaptive guaranteed-performance consensus protocol was presented by adjusting the communication weights among agents in the system topology. Sufficient conditions for adaptive guaranteed-performance consensus were obtained and the guaranteed-performance cost was deduced. Then in order to indicate the convergence speed of multiagent systems, the convergence coefficient was defined, and it was proved that the convergence speed can be approximately linear adjustable by changing the adaptive control gain.

This paper assumes that the research objective is first-order linear multiagent systems. The dynamics of each agent is described as the first-order integrators. In this case, the adaptive guaranteed-performance consensus analysis can be simplified by the specific structure of the multiagent system. However, due to the wide existence of nonlinear dynamics in practical systems, it is very meaningful to study nonlinear multiagent systems. Thus, we will focus on adaptive guaranteed-performance consensus problems for nonlinear multiagent systems by the Lipschitz condition in the future.

All the data in the simulation is included within this article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

I would like to express my faithful gratitude to all those who helped me during the writing of this paper. I gratefully acknowledge the help of my partners, Mr. Ning Cai and Mr. Jianxiang Xi, who have offered me patient instruction in the academic studies. This work is supported by National Natural Science Foundation (NNSF) of China (Grants 61867005 and 61763040), by Fundamental Research Funds for the Central Universities (Grants 2019RC29 and 31920180115), by the Gansu Provincial First-Class Discipline Program of Northwest Minzu University (Grant 11080305), and by Research Funds of SEAC China for the New Silk Road Economic Belt (Grant 2018-GMH-001).