Further properties of second-order multi-agent flocking under Olfati-Saber's algorithms

In this paper, we revisit the flocking control algorithms suggested by Olfati-Saber for the second-order multi-agent networks, in which the multi-agents are driven by the distributed algorithms installed on each and all agents that are based merely on local measurements of neighboring multi-agent position and velocity vectors. It has been shown that by under appropriate initial conditions about the agent positions and velocities, the concerned multi-agent systems eventually run into flocking formation, namely α-lattice, by means of the Olfati-Saber control algorithms. This paper is devoted to probe into additional features and properties under the same flocking algorithms. What is revealed further in this study includes: the average flocking trajectory, its controllability and geometrical facts, steady-state features and the modes of the structural dynamics. Moreover, possible inter-agent collision is verified via the variation-of-constant formula and the Gronwall inequality when the agents initially aggregate too densely. Numerical examples are sketched to illustrate the main results.