Event-triggered bipartite consensus of single-integrator multi-agent systems is investigated in the presence of measurement noise. A time-varying gain function is proposed in the event-triggered bipartite consensus protocol to reduce the negative effects of the noise corrupted information processed by the agents. Using the state transition matrix, It
Recent years have witnessed the great achievements in studying the consensus problem of multi-agent systems (MASs) which has broad applications in various fields [
It is worth noting that the above literatures mainly focus on continuous feedback protocols, where the agent state is monitored continuously and its controller is updated all the time. However, updating the controller in real-time easily increases the computational burden. Therefore, reducing the update frequency for a trade-off between the system performance and the resource usage is usually desired. This requirement then naturally brings event-triggered schemes into consideration, which updates only at some predetermined discrete time instants. Event-triggered techniques have already been widely used in traditional consensus problems of MASs [
In another parallel line, measurement noise is unavoidable in practice, making the investigation on the event-triggered bipartite consensus of MASs with noise even interesting. In fact, studies on bipartite consensus with measurement noise can be found in [
In this paper, we investigate event-triggered bipartite consensus for single-integrator MASs with measurement noise. A time-varying control gain is introduced into the event-triggered protocols, leading to a time-varying closed-loop system. With the help of the state transition matrix and stochastic analysis theory, the closed-loop system is analyzed. Necessary and sufficient conditions for the system to achieve mean square bipartite consensus based on event-triggered protocols are given. We find that the communication topology being structurally balanced and containing a spanning tree are necessary and sufficient for ensuring a mean square bipartite consensus based on event-triggered protocols.
The communication relations among
If
Consider a MAS described by
Since communication is often disturbed by measurement noise, we assume the
As far as we know the existing results [
Let
Let
We introduce the event-triggered condition
To analyze the closed-loop system in (
The following lemma plays an important role in the following section.
Given linear time-varying system
If the event-triggered protocol (
From the above condition, Definition
Let
If
If
Since
By It
By
Let
Let
In this section, we give necessary and sufficient conditions for the proposed event-triggered protocols to guarantee a mean square bipartite consensus.
The event-triggered protocol in (
Let
Then
by (
By It
Combining this with
We assume
It is easy to obtain that
Let
Necessity.
Let
Let algebra multiplicity of eigenvalue 0 be
Noticing that
By
From Theorem
From Theorem
To demonstrate the developed result in the preceding, we consider an MAS of six agents, whose dynamics satisfy the system in (
Communication graph
State trajectories of six agents.
Control inputs of six agents.
The evolution of error norm.
Mean square bipartite consensus problem of single-integrator MASs is investigated in the context of event-triggered control and measurement noise. By using time-varying gain, an event-triggered bipartite consensus protocol is proposed under measurement noise, with which the controller update frequency is reduced. With given necessary and sufficient conditions on protocol gain and communication topology, the MAS is proved to achieve event-triggered bipartite consensus. The simulation shows that the system will not show Zeno behavior.
The Matlab based models used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China under Grants 61104136 and 61673350, Postgraduate Education Innovation Program of Shandong Province under Grant no. SDYY16088, and the Young Teacher Capability Enhancement Program for Domestic Study, Qufu Normal University.