Analysis of Flocking of Cooperative Multiple Inertial Agents via A Geometric Decomposition Technique

In this paper, we consider flocking of multiple inertial agents with second-order dynamics. For a single agent, its state is therefore velocity and position. There exists both velocity coupling and position coupling between agents that are not necessarily equal. The nonequal couplings are distinguished here, instead of the common assumption of the equal velocity coupling and position coupling in most literature, since they play different roles in the system dynamics. The main contributions are in two aspects: first, we provide a general geometric decomposition approach for analyzing such systems of the agents. Then, we provide some stability results via Lyapunov analysis as a function of couplings and gains that generalize existing results in this area, which are especially useful when the couplings are partially known. Although the stability results are only sufficient, they serve as important complements of the eigenvalue analysis, which generally requires complete knowledge of the couplings in the eigenvalue analysis.