Distributed Concurrent Targeting for Linear Arrays of Point Sources

Abstract

Motivated by practical applications in satellite formations and antenna arrays etc., the problem of targeting a linear array of point sources at one common point of interest is formulated and then solved using a novel distributed control strategy. These point sources are located collinearly and the two at the two ends orient readily to the target point. The other point sources have to rely on sensing the changes of the relative orientation angles of their nearest neighbors to adjust their own orientations; we rigorously prove that under our control law using only local information, their orientation lines will intersect at the same point of concurrency as the two point sources at the two ends. The crucial idea behind our designed control law is the intuitive argument from plane geometry that reducing the differences between the distances to the baseline of the pairwise intersection points of the orientation lines helps realizing concurrent targeting. This idea is further utilized to construct the key argument in our analysis about the boundedness and the exponential convergence speed of the orientation angles. Numerical simulations are used to validate the effectiveness of our control strategy.