Aggregation of Swarms With Group Leaders Using Nearest Neighbors Information

In this paper, the stability of the aggregation of swarms is considered by employing the local information. The leaders and the followers are included in the proposed swarms, and only the leaders have the knowledge about the environment. Thus, the next position of each leader is decided by the information of the environment and the position of its neighbors, while the next position of each follower is decided only by the position of its neighbors. Under the assumption that the gradient of the environment is bounded, it is shown that the collective behavior of the swarms is stable, and further, all of the individuals finally aggregate around the center of the group´s position at the same speed. The obtained results are illustrated by a numerical example.