Leader-follower formation via complex Laplacian

摘要: The paper introduces complex-valued Laplacians for graphs whose edges are attributed with complex weights and studies the leader-follower formation problem based on Laplacians. main goal is to control shape of a planar point agents in plane using simple linear interaction rules related We present characterization that preserve specific as an equilibrium solution both single integrator kinematics double dynamics. Planar formations under study subject translation, rotation, scaling plane, but can be determined by two co-leaders networks. Furthermore, when Laplacian does not result asymptotically stable behavior multi-agent system, we show stabilizing matrix, which updates weights, exists stabilize system while preserving formation. Also, algorithms provided find matrices. Finally, simulations presented illustrate our results.