Adaptive time-varying formation control for high-order linear multi-agent systems with directed interaction topology

In this paper, distributed time-varying formation control problems for general high-order linear time-invariant multi-agent systems with directed interaction topologies are addressed using an adaptive based approach. Firstly, a distributed adaptive time-varying formation control protocol is proposed, which assigns a time-varying coupling weight for each node in the interaction topology. Then an algorithm is presented to design the distributed adaptive formation control protocol without using any global information about the interaction topology. A description of the feasible time-varying formation set is given. Moreover, sufficient condition for high-order linear time-invariant multi-agent systems to achieve the predefined time-varying formation under the designed protocol are derived based on the Lyapunov theory. Finally, a numerical example is given to illustrate the theoretical results.

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