高阶群系统编队合围分析与综合

Theories on formation control and containment of high-order swarm systems (or called as multi-agent systems) have broad potential applications in military and civilian fields, such as formation control of multiple unmanned aerial vehicles, movement of multiple robots in hazardous environment, environment monitoring, and etc. This project aims at dealing with the following problems for high-order linear time-invariant swarm systems with homogeneous agents and general directed interaction topologies. Firstly, analysis and design problems for swarm systems with and without communication time delays to achieve state/output time-varying formation are investigated. Necessary and sufficient criteria for achieving formation and for formation feasibility are presented respectively. An explicit expression of the formation center function is shown, and approaches to expand the feasible formation set and to determine the gain matrices in the protocols are presented. Secondly, analysis and design problems for swarm systems to achieve state/output containment are studied. Necessary and sufficient criteria for achieving state/output containment are proposed and approaches to determine the gain matrices in the protocol are given. Finally, analysis and design problems for swarm systems to achieve state/output formation-containment are discussed. Sufficient criteria for achieving state/output formation-containment are derived and approaches to determine the gain matrices in the formation-containment protocol are presented.

高阶群系统(或称多主体系统)编队合围理论在无人机群编队控制、多机器人障碍环境下移动、环境监测等军事和民用领域有着广阔的应用前景。本项目拟针对具有高阶线性定常同构主体和有向作用拓扑的群系统，首先研究在有/无时延条件下状态/输出时变编队的分析和设计问题，给出实现编队的充要条件和编队可行性的充要判据，给出编队中心函数的显示表达式，并提出扩展可行编队集合的方法和控制协议中增益矩阵的设计方法；其次，研究状态/输出合围的分析和设计问题，给出实现状态/输出合围的充要条件和确定控制协议中增益矩阵的方法；最后，研究状态/输出编队-合围的分析和设计问题，给出实现状态/输出编队-合围的条件和控制协议中增益矩阵的设计方法。

高阶群系统编队合围理论在无人机群编队控制、多机器人协作等军事和民用领域有着广阔的应用前景。本项目针对具有高阶线性定常同构主体和有向作用拓扑的一般高阶群系统，首先针对编队控制问题，分别研究了在有/无通讯时延情况下实现状态/输出时变编队的分析问题、编队可行性的分析问题和实现时变编队的控制协议增益矩阵的设计问题；研究了编队中心函数显示表达和扩展可行编队集合的问题。其次针对合围问题，研究了状态/输出合围的分析问题和实现合围的控制协议增益矩阵的设计问题。进而针对编队-合围问题，研究了状态/输出编队-合围的分析问题和实现编队-合围的控制协议增益矩阵的设计问题。.所研究的问题具有一般性，所取得的理论结果具有一般性和创新性。首次给出了一般高阶线性定常群系统扩展可行时变编队集合的方法。首次给出了一般高阶线性定常群系统实现输出合围的充要条件以及实现状态/输出编队-合围的条件。.为了对所取得的一般性理论成果的实用性进行检验，我们选择无人机集群系统为应用对象，得到了实现时变编队的充要条件及时变编队可行性的条件，分别进行了多架四旋翼无人机在有向作用拓扑及拓扑切换条件下实现时变编队的多组飞行实验，取得了良好的控制效果。相关成果分别于2015和2016年发表在IEEE Transactions on Control Systems Technology和Control Engineering Practice上。前者已经被SCI他引98次，后者被SCI他引46次，两篇论文均成为ESI高被引论文。此外得到了具有切换拓扑的二阶多主体系统实现时变编队跟踪的充分必要条件，并在室外实现了多架四旋翼无人机对目标的包围，相关成果于2017年发表在IEEE Transactions on Industrial Electronics上，被SCI他引11次，也已成为高被引论文。.在本项目的资助下，发表SCI检索论文14篇，EI期刊论文2篇，发表EI会议论文16篇。申请专利1项。培养博士生3名，硕士生7名。获得中国自动化学会优秀博士学位论文提名奖1项，获得2017年中国控制会议张贴论文奖1项。