Distributed Pinning-Controlled Flocking with a Virtual Leader

Abstract

This chapter introduces a flocking control problem in the presence of a virtual leader and only a fraction of informed agents. We solve the distributed collective tracking problem via pinning control approach. We first show that, even when only a fraction of agents are informed, the proposed flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be influenced by the informed agents from time to time during the evolution. In the situation where the virtual leader travels with a varying velocity, we propose a novel flocking algorithm and show that the proposed flocking algorithm enables the asymptotic tracking of the virtual leader. That is, the position and velocity of the center of mass of all agents will converge exponentially to those of the virtual leader. The convergent rate is also given. Numerical simulation demonstrates that a very small group of the informed agents can cause most of the agents to move with the desired velocity and the larger the informed group is the bigger portion of agents will move with the desired velocity.