Distributed Time-Varying Formation Tracking Analysis and Design for Second-Order Multi-Agent Systems

Distributed time-varying formation tracking analysis and design problems for second-order multi-agent systems with one leader are studied respectively, where the states of followers form a predefined time-varying formation while tracking the state of the leader. Different from the previous results on formation tracking control, the formation for the followers can be described by specified time-varying vectors and the trajectory of the leader can also be time-varying. A distributed formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for second-order multi-agent systems with one leader to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraint is also given. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems and consensus tracking problems for second-order multi-agent systems with one target/leader. An application in the target enclosing of multiple vehicles is provided to demonstrate the effectiveness of the theoretical results.