Time-Varying Formation Tracking for Linear Multiagent Systems With Multiple Leaders

Time-varying formation tracking problems for linear multiagent systems with multiple leaders are studied, where the states of followers form a predefined time-varying formation while tracking the convex combination of the states of multiple leaders. Followers are classified into well-informed ones and uninformed ones, where the neighbor set of the former contains all the leaders, whereas the latter contains no leaders. A formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for multiagent systems with multiple leaders to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraints are also given. An approach to design the formation tracking protocol is presented by solving an algebraic Riccati equation. The obtained results can be applied to deal with time-varying formation tracking problems, target enclosing problems, and consensus tracking problems for linear multiagent systems with one or multiple targets/leaders. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results.