Time-varying formation control for high-order linear swarm systems with switching interaction topologies

Time-varying formation control problems for high-order linear time-invariant swarm systems with switching interaction topologies are investigated. A general formation control protocol is proposed firstly. Then using a consensus based approach, necessary and sufficient conditions for swarm systems with switching interaction topologies to achieve a given time-varying formation are presented. An explicit expression of the time-varying formation reference function is given. It is revealed that the switching interaction topologies have no effect on the formation reference function and the motion modes of the formation reference can be specified. Furthermore, necessary and sufficient conditions for formation feasibility are presented. An approach to expand the feasible formation set is given and an algorithm to design the protocol for swarm systems with switching interaction topologies to achieve time-varying formations is provided. Finally, numerical simulations are presented to demonstrate theoretical results.