一类复杂通信条件下高阶线性群系统编队控制

doi:10.13700/j.bh.1001-5965.2019.0302

北京航空航天大学学报 ›› 2020, Vol. 46 ›› Issue (4): 769-780.doi: 10.13700/j.bh.1001-5965.2019.0302

一类复杂通信条件下高阶线性群系统编队控制

石晓航¹, 张庆杰², 吕俊伟³

1. 海军大连舰艇学院, 大连 116001;
2. 空军航空大学, 长春 130022;
3. 海军航空大学, 烟台 264001

收稿日期:2019-06-17 发布日期:2020-04-21
通讯作者: 张庆杰 E-mail:nudtzhang@hotmail.com
作者简介:石晓航,男,博士,讲师。主要研究方向:群系统编队控制;张庆杰,男,博士,副教授,硕士生导师。主要研究方向:群系统编队控制。
基金资助:
国家自然科学基金（61004002）；航空科学基金（20155884012）

Formation control for high-order linear swarm systems with complex communication conditions

SHI Xiaohang¹, ZHANG Qingjie², LYU Junwei³

1. Dalian Naval Academy, Dalian 116001, China;
2. Aviation University of Air Force, Changchun 130022, China;
3. Naval Aviation University, Yantai 264001, China

Received:2019-06-17 Published:2020-04-21
Supported by:
National Natural Science Foundation of China (61004002); Aeronautical Science Foundation of China (20155884012)

摘要/Abstract

摘要： 针对时变时延、拓扑不确定和外部扰动等复杂通信条件下的高阶线性群系统编队控制问题进行研究。首先，建立了群系统编队控制问题的数学描述，并基于一致性最近邻原则给出了编队控制协议框架。其次，提出了群系统实现编队的充要条件。通过状态分解和变量代换，给出了约束条件下，编队控制协议的设计方法。同时，为得到群系统所允许最大时延边界，引入自由权矩阵，得到了保守性较小的线性矩阵不等式（LMI）判据条件。仿真实验验证了编队控制方法对于有界时变时延、拓扑不确定以及外部扰动具有一定的鲁棒性。

关键词: 编队控制, 高阶群系统, 时变时延, 拓扑不确定, 外部扰动, 自由权矩阵

Abstract: The formation control problems for high-order linear swarm systems with time-varying delays, topology uncertainties and external disturbances are investigated. Firstly, the mathematical description of the formation control for swarm systems is established, and the formation control protocol is proposed based on the consensus nearest neighbor principle. Secondly, the necessary and sufficient conditions for swarm systems to achieve the formation are presented. By decomposing the state and using the variable substitution method, the design method of formation protocol is given under the constrained conditions. Furthermore, in order to get the upper bound of the time-varying delays, the free-weighting matrices are introduced, and the linear matrix inequality (LMI) criteria with lower conservation are obtained. Finally, numerical examples and simulation results are given to demonstrate the effectiveness of the proposed method. The formation control method is robust for bounded time-varying delays, topology uncertainties and external disturbances.

Key words: formation control, high-order swarm systems, time-varying delays, topology uncertainties, external disturbances, free-weighting matrices

中图分类号:

TP273

石晓航, 张庆杰, 吕俊伟. 一类复杂通信条件下高阶线性群系统编队控制[J]. 北京航空航天大学学报, 2020, 46(4): 769-780.

SHI Xiaohang, ZHANG Qingjie, LYU Junwei. Formation control for high-order linear swarm systems with complex communication conditions[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(4): 769-780.

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一类复杂通信条件下高阶线性群系统编队控制

Formation control for high-order linear swarm systems with complex communication conditions

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