Time-varying formation feasibility analysis for linear multi-agent systems with time delays and switching graphs

Time-varying formation control, formation tracking control, and formation-containment control for multi-agent systems have attracted significant attention recently, where the formation feasibility is a crucial common problem. For a given linear multi-agent system, not all the time-varying formations can be realized due to the dynamic restriction of each agent. The formation feasibility constraint reveals the requirement on the desired time-varying formation to be compatible with the agent dynamics. Formation reference is a representation for the macroscopic movement of the whole multi-agent system. Novel features of the formation feasibility constraint and the formation reference are the main focus of the current paper. Firstly, a timedelayed formation control protocol with switching directed topologies is constructed using local neighboring information. Then time-varying formation feasibility constraint is derived based on nonsingular transformations. It is proven that the time-varying formation feasibility constraint is independent of the time-varying delays and the switching directed topologies. Moreover, an explicit expression of the formation reference function is proposed. It is shown that neither the time-varying delays nor the switching directed topologies have influence on the obtained formation reference function.