This paper deals with the consensus problem of linear multi-agent systems with actuator faults. A fault estimator based consensus protocol is provided, together with a convergence analysis. It is shown that the consensus errors of all agents will converge to a small set around the origin, if parameters in the consensus protocol are properly chosen. A numerical example is given to illustrate the effectiveness of the proposed protocol.

Recently, distributed consensus problems for multi-agent systems have become a hot research area in the control theory community [

Fault detection and fault accommodation are very important problems for control systems [

The fault tolerant consensus problem for high-order linear multi-agent systems has not been considered in the literature, which motivated the work in this paper. In this paper, consensus problems will be considered for linear multi-agent systems with actuator faults. A fault estimator is provided, based on which a consensus protocol is derived. It is proved that consensus error can converge to a small set around the origin, if parameters in the fault estimator and the consensus protocol are properly chosen. The rest of the paper is organized as follows. Section

Consider a team of

Assume that

Assumption

The communication topology among the

We say algorithm

The objective of this paper is to derive a consensus protocol

This section gives the fault tolerant consensus protocol for multi-agent systems described in the last section. Before giving the consensus protocol, we give the fault estimator first.

Consider the following fault estimator, which is motivated by the fault estimator in [

Define

The proof is similar to the proof of Theorem 1 in [

Under Assumption

It can be seen that

Let

The eigenvalues of

There exists an orthogonal matrix

Next, we give the main results of this paper.

Suppose the undirected graph

Suppose that the communication graph is connected; the nonzero eigenvalues of

Define

Consider the following Lyapunov function:

Notice that

Theorem

Consider a multi-agent system consisting of

The network topology associated with agents

Position responses of agents 1–4.

Velocity responses of agents 1–4.

The fault-tolerant consensus problem for multi-agent systems with actuator faults was considered. A fault estimator based consensus protocol is provided, together with a sufficient condition under which the consensus can be achieved. It is proved that consensus errors of all agents can converge to a small set around the origin. The numerical example confirmed the proposed theoretical results. In practice, many systems have stochastic Markovian jumping dynamics [

This study was supported by National Natural Science Foundation of China under Grants 61203024, 61100116, 61374063, and 61304249, Natural Science Fundamental Research Project of Jiangsu Colleges and Universities under Grant 12KJB120001, and the Natural Science Foundation of Jiangsu Province of China under Grant BK2011492.