This paper investigates the distributed consensus problem of multiagent systems with semi-Markovian jumping dynamics in the mean-square sense. Moreover, the mode-dependent communication topologies and sampled-data consensus protocol over the networks are considered. By semi-Markov jump theory, the consensus problem is first transformed into a mean-square stability problem. Then, sufficient conditions are established with the designed mode-dependent consensus protocol. Finally, a numerical example is provided for verifying the effectiveness of our theoretical results.
Owing to the rapid development of computer science and network technology, the multiagent systems (MASs) have become a hot research topic with significant applications including mobile robots [
On the other hand, it is noticed that dynamical systems may display mode switching features by abrupt phenomena, which gives rise to researches on switched systems [
In response to the above discussions, this paper solves the distributed consensus problem of semi-Markovian jumping MASs with mode-dependent topologies and information exchanges by employing the key idea from semi-Markovian jumping systems. The main contributions of our paper can be summarized as follows. Firstly, a novel model of semi-Markovian jumping MASs with mode-dependent topologies is proposed for better describing the agent dynamics. Secondly, the distributed mode-dependent consensus protocol with sampled-data information exchanges is designed for guaranteeing the mean-square consensus, which is more applicable for the network environment. Finally, based on model transformation, sufficient consensus criteria are established by applying the mode-dependent Lyapunov-Krasovskii method in the form of linear matrix inequalities (LMIs).
The rest of our paper is outlined as follows. In Section
Fix a probability space
The directed graph
Consider the semi-Markovian jumping MASs consisting of
It is worth mentioning that the communication topologies could dynamically switch according to the different modes of multiagent systems, which leads to the semi-Markovian jumping mode-dependent topologies. Without loss of generality, it is assumed that all the switching modes can be detected to the agent dynamics and the communication topologies.
The consensus is said to be achieved in the mean-square sense if and only if it holds that
The following lemma is given for the subsequent analysis.
For matrix
In this paper, the sampled-data communication strategy with different modes is adopted. Suppose that the MASs communicate with their local neighbors over the communication network according to a global discrete-time sequence:
The following mode-dependent consensus protocol is designed:
It is assumed that the semi-Markovian jumping modes can be detected at the sampling instances, such that the system modes can be obtained by the agents and the communication topologies based on sampled-data communication strategy.
Consequently, the closed-loop dynamics of the MASs can be obtained as follows:
It can be verified that when
By defining
Thus, it can be obtained that the consensus can be achieved when
To this end, denote
Based on the above consensus protocol, the following theorems are derived for the consensus analysis and synthesis of semi-Markovian jumping MASs.
For given scalar
For each mode
The weak infinitesimal operator
Then, it can be derived that
By Lemma
Thus, one has
It follows by Schur complement that
Noticing the fact that
For given scalar
Based on Theorem
Letting
It can be found that the dimensions of LMIs are related to the
In this section, an illustrative example with simulation results is provided for showing our proposed consensus design.
Consider the semi-Markovian jumping MASs with four agents and two jumping modes.
The transition rates are assumed to be
The agent dynamics are described by the following parameters:
The communication topologies with directed spanning trees are depicted in Figures
The communication topology with mode 1.
The communication topology with mode 2.
With the above parameters, the mode-dependent consensus control input gains of the MASs can be calculated by solving the LMIs in Theorem
As a result, the consensus state responses of the semi-Markovian jumping MASs by our designed consensus control input gains can be seen in Figure
The state responses of the semi-Markovian jumping MASs.
This paper focuses on the distributed consensus of semi-Markovian jumping MASs with mode-dependent communication topologies. The mode-dependent consensus protocol with sampled-data information is proposed. On the basis of model transformation and Lyapunov-Krasovskii method, sufficient consensus criteria are derived in the mean-square sense and the mode-dependent consensus gains are designed with LMIs. In the end, a simulation example is given for validating the effectiveness of our theoretical results. Our future work would encompass investigating the consensus of semi-Markovian jumping MASs under constrained network environments.
The data used to support the findings of this study are included within the article.
The author declares that he has no conflicts of interest.