Time-varying formation control for linear multi-agent systems with distributed adaptive protocols

Distributed time-varying formation control problems are considered for general high-order linear time-invariant multiagent systems using an adaptive based approach with undirected interaction topology. Based on relative neighboring state information, by distributing each node a time-varying coupling weight, a distributed adaptive control protocol is proposed for achieving time-varying formation. A set of the feasible time-varying formation constraint is given. It is revealed that the formation can be specified by piecewise continuously differentiable vectors, under the distributed adaptive formation control protocol, and no global information about the interaction topology is required. Then an algorithm is presented to determine the distributed adaptive formation control protocol. On the basis of the Lyapunov theory, the stability of the algorithm is investigated. A numerical simulation example is finally given to verify the theoretical results.