On Stability Analysis of Predictive Flocking Using N-Paths

Most publications in the field of model predictive flocking (MPF) present frameworks without providing stability analyses for the proposed schemes. In those providing stability results, one specific line of reasoning is based on the geometric properties of the optimal state sequences, so-called
$N$
-paths. This method is used in several publications to show stability for centralized and distributed MPF schemes. In this paper, we critically discuss this line of reasoning and point out several errors in the
$N$
-path-based analysis. As incorrect statements in assumptions and lemmas cause the lines of reasoning to break, this raises the question of whether the N-path-based line of reasoning is suitable for the MPF stability analysis in general.