Flocking of multi-agents with a virtual leader part I: with a minority of informed agents

All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multi-agent systems. Under these assumptions, Olfati-Saber in a recent IEEE Transactions on Automatic Control paper proposed a flocking algorithm which by incorporating a navigational feedback enables a group of agents to track a virtual leader. This paper revisits the problem of multi-agent flocking in the absence of the above two assumptions. In particular, in Part I, we show that, even when only a fraction of agents are informed, the Olfati-Saber 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 directly or indirectly influenced by the informed agents during the evolution. 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. In Part II, we will address the situation when the virtual leader travels at a varying velocity.