Formation Tracking for High-Order Time-Invariant Swarm Systems with Limited Energy and Fixed Topologies

Abstract EN

The current paper investigates design and analysis problems of formation tracking for high-order linear time-invariant swarm systems, where communication topologies among agents have leader-following structures and the whole energy supply is limited.

Firstly, the communication topology of a swarm system is depicted by a directed graph with a spanning tree, where the communication channels from the leader to followers are directional and the communication channels among followers are bidirectional, and a new formation tracking protocol with an energy integral term and a given upper bound is proposed to achieve formation tracking with the limited energy.

Then, sufficient conditions for time-varying formation tracking design and analysis with the limited energy are presented, respectively, which include two/three linear matrix inequality constraints associated with the maximum and minimum nonzero eigenvalues of the Laplacian matrix of a communication topology.

Especially, time-invariant formation tracking criteria are further deduced.

Finally, two numerical examples are revealed to verify main theoretical conclusions.