In this paper, the time-varying formation and time-varying formation tracking problems are solved for linear multi-agent systems over digraphs without the knowledge of the eigenvalues of the Laplacian matrix associated to the digraph. The solution to these problems relies on a framework that generalizes the directed spanning tree adaptive method, which was originally limited to consensus problems. Necessary and sufficient conditions for the existence of solutions to the formation problems are derived. Asymptotic convergence of the formation errors is proved via graph theory and Lyapunov analysis.
Decentralized design of consensus protocols with minimal communication links based on directed spanning tree
College of Artificial Intelligence and Automation, Beijing University of Technology（北京工业大学人工智能与自动化学院）；Engineering Research Center of Digital Community, Ministry of Education（教育部数字社区工程研究中心）
Designing Distributed Fixed-Time Consensus Protocols for Linear Multi-Agent Systems Over Directed Graphs
School of Automation, Northwestern Polytechnical University（西北工业大学自动化学院）；Department of Electronic Engineering, City University of Hong Kong（香港城市大学电子工程系）
Non-trivial consensus on directed signed matrix-weighted networks with compound measurement noises and time-varying topologies
School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机科学与软件工程学院）
A unified framework of fully distributed adaptive output time-varying formation control for linear multi-agent systems: an observer viewpoint
Ecole Centrale de Lille（里尔中央理工学院）；Beihang University（北京航空航天大学）；Beijing Engineering Center for Clean Energy & High Efficient Power, Beihang University（北京航空航天大学清洁能源与高效动力工程中心）；Department of Mathematics, Beijing Jiaotong University（北京交通大学数学系）；CRIStAL, UMR CNRS 9189, Ecole Centrale de Lille（里尔中央理工学院 CRIStAL 实验室）
Event-triggered consensus of multi-agent systems under directed topology based on periodic sampled-data
School of Mathematics and Statistics, Qingdao University（青岛大学数学与统计学院）；College of Automation and Electrical Engineering, Qingdao University（青岛大学自动化与电气工程学院）；School of Control Science and Engineering, Shandong University（山东大学控制科学与工程学院）
