【Paper】2014_A distributed event-triggered transmission strategy for sampled-data consensus of multi-

Guo G, Ding L, Han Q L. A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems[J]. Automatica, 2014, 50(5): 1489-1496.

Related: 【Paper】2020_Leader-following consensus for multi-agent systems subject to cyber attacks Dynamic even

1. Introduction

2. A novel distributed event-triggered transmission strategy

For this purpose, we present the novel distributed event-triggered transmission strategy for the distributed multi-agent system, whose framework is illustrated in Fig. 1.

In this framework, whether or not sampled-data of agent $i$ should be broadcasted at the sampling instant $kh$ ($k\in \mathbb{N}$ ) depends on whenever its threshold is violated.

More specifically, it is assumed that the sampler is time-driven, the storer, the controller and the actuator with ZOH (zero-order hold) are all event-driven and all the sampled-data packets are transmitted with their time stamps.

The state of each agent $i$ is sampled by a sampler at a constant sampling period $h>0$.

The sampled-data $x_i(kh)(k\in \mathbb{N})$ of agent $i$ can be successfully sent to its distributed event processor (DEP) embedding an event-triggered condition.

Here, the DEP’s execution of each agent $i$ involves three tasks:

• (i) receiving the sampled-data from agent $i$ and its storer at each sampling instant;
• (ii) processing the received sampled-data with respect to the event-triggered condition; and
• (iii) generating a trigger signal to the event trigger when a threshold is violated.

Once the event trigger receives a trigger signal, the sampled-data of agent $i$ is authorized to be broadcasted to the storers of its own and its neighbors’.

It should be pointed out that the storer is employed to gather the sampled-data of agent $i$ and its neighbors and to immediately update its information as soon as measuring new sampled-data from agent $i$ and its neighbors.

Then, the controller of agent i updates its input by using the received sampled-data from the storer, which implies that the controller update of agent $i$ is driven at both its own and neighbors’ event instants.

Then, the output of the controller of agent $i$ is sent to the actuator with ZOH, where ZOH is used to keep the control input of agent $i$ constant when no newest sampled-data from the controller of agent $i$ arrives.

$$\begin{array}{r}{t}_{m+1}^{i}h=t_m^{i}h+\underset{l_i\ge 1}{\min }\left\{l_{i}h|{\chi }_i^{\text{T}}(t_m^{i}h+l_{i}h)\Phi {\chi }_i(t_m^{i}h+l_{i}h)\ge {\sigma }_i{y}_i^{\text{T}}(t_m^{i}h+l_{i}h)\Phi y_i(t_m^{i}h+l_{i}h)\right\}\end{array}\text{\hspace{1em}(3)}$$

where
$l_i\in \mathbb{N}$,
$\sigma >0$ is a threshold parameter,
$\Phi >0$ is a weighting matrix,
${\chi }_i(t_m^{i}h+l_{i}h)=x_i(t_m^{i}h+l_{i}h)-x_i(t_m^{i}h)$ and
$y_i(t_m^{i}h+l_{i}h)={\sum }_{j=1}^N{w}_{ij}[x_i(t_m^{i}h)-x_j(t_{m_j^{\prime }}^{j}h)]$ with
$m_j^{\prime }\triangleq {\mathrm{argmin}}_p\left\{t_m^i+l_i-t_p^j|t_m^i+l_i>t_p^j,p\in \mathbb{N}\right\}$.

Apparently, one can see from (2) that, at the $k$th sampling instant, the event-triggered condition for agent $i$ is closely related to the sampled-data error
${\chi }_i(t_m^{i}h+l_{i}h)$ and the sampled-data
$y_i(t_m^{i}h+l_{i}h)$ including the latest transmitted sampled-data
$x_i(t_m^{i}h)$ of agent $i$ and the latest transmitted sampled-data
$x_j(t_{m_j^{\prime }}^{j}h)$ of its neighbors.

Then, we propose the following new sampled-data consensus protocol

自己复现的带触发结果如下，对应程序 main_ET.m

Ref