ABSTRACT
Time-varying formation analysis and design problems for homogeneous swarm systems with general linear dynamics and switching directed interaction topologies are investigated in this chapter firstly. Necessary and sufficient conditions to achieve time-varying formations are proposed, where a description of the feasible time-varying formation set and approaches to expand the feasible formation set are given. An algorithm to design the formation control protocol for homogeneous swarm systems is presented. Then, time-varying formation tracking problems for homogeneous linear swarm systems with multiple leaders are studied based on the well-informed follower assumption. A formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for swarm systems with multiple leaders to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix. An approach to design the formation tracking protocol is presented by solving an algebraic Riccati equation.
