Distributed adaptive time-varying formation for multi-agent systems with general high-order linear time-invariant dynamics

This paper studies distributed time-varying formation control problems for general high-order linear time-invariant (LTI) multi-agent systems using an adaptive based approach. Firstly, a time-varying formation control protocol is constructed by the states of neighboring agents, which the adaptive gain scheduling technique is employed to estimate the coupling weights between neighboring agents. Different from the existing results on formation control, the formation can be specified by piecewise continuously differentiable vectors and no global information about the interaction topologies is required. Then an algorithm with two steps is presented to design the distributed adaptive formation control protocol, where a description of the feasible time-varying formation set is given. The stability of the algorithm is proved using the Lyapunov theory. It is shown that if the predefined time-varying formation belongs to the feasible formation set and each agent is stabilizable, then time-varying formation can be achieved by general high-order LTI multi-agent systems using the distributed adaptive formation protocol designed in the proposed algorithm. Finally, numerical examples are given to demonstrate the effectiveness of the theoretical results.