Time-varying output formation control for high-order linear time-invariant swarm systems

Formation control of swarm systems has gained considerable attention from scientific communities due to its potential applications in various areas. In practical applications, the dynamics of each agent may be of high order and only the outputs of all agents are required to achieve time-varying formations. Therefore, this paper focuses on time-varying output formation control problems for high-order linear time-invariant swarm systems with directed interaction topologies. A general output formation protocol is proposed based on the relative outputs of neighboring agents. Necessary and sufficient conditions for swarm systems to achieve time-varying output formations are presented using a consensus based approach. An explicit expression of the output formation reference function is given. For a swarm system, whether or not a desired output formation is feasible is a crucial problem. Based on partial stability theory, necessary and sufficient conditions for output formation feasibility are derived. Approaches to expand the feasible time-varying output formation set and an algorithm to design the protocol for swarm systems to achieve time-varying output formation are presented respectively. Finally, theoretical results are demonstrated by numerical simulations.