Open Access
 Issue JNWPU Volume 38, Number 6, December 2020 1139 - 1145 https://doi.org/10.1051/jnwpu/20203861139 02 February 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1 合围点部署问题

### 1.1 问题描述

 图1多智能体协同围捕单个目标

### 1.2 问题建模

 图2多智能体合围点在以目标为中心的圆上的部署

## 3 收敛性分析

### 3.1 渐进收敛性分析

1) 当2≤in-1时, 由公式(1)、(3)、(5)可得

2) 当i=1时, 有

3) 同理, 当i=n时, 有

di(k), i=1, 2, …, n渐进一致可知, 覆盖代价函数T(k)将渐进收敛到零。

### 3.2 有限时间收敛性分析

t(k)≥(1-τ)T*后, τK(k)=1, 由于在此之前邻接角距di(i=1, 2, …, n)已实现精确一致, 故系统将临界稳定于平衡状态。

## 4 仿真验证

 图3多智能体合围点的初始位置分布
 图4多智能体合围点的最终位置分布
 图53组实验的覆盖代价函数收敛过程对比
 图6实验1仿真结果
 图7实验2仿真结果
 图8实验3仿真结果

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## All Figures

 图1多智能体协同围捕单个目标 In the text
 图2多智能体合围点在以目标为中心的圆上的部署 In the text
 图3多智能体合围点的初始位置分布 In the text
 图4多智能体合围点的最终位置分布 In the text
 图53组实验的覆盖代价函数收敛过程对比 In the text
 图6实验1仿真结果 In the text
 图7实验2仿真结果 In the text
 图8实验3仿真结果 In the text

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