Flocking Analysis and Comparison in Simplex Multi-Agent Systems under Matrix-Weighting Hölder Norms

Regarding flocking filing specification in what we term simplex multi-agent systems that are driven only with local position measurements and corresponding speed estimates via distributed observers, together with compatible matrix-weighting Hvlder norms, a class of generalized artificial potential functions (GAPF) are defined and flocking control algorithms are discussed in this paper. Matrix-weighting Hvlder norms have more elaborate and subtle geometrical and algebraic structure and significance in their gradients and time derivatives. It is shown in this study that if the GAPE is defined based on matrix-weighting Hvlder norms, these mathematical merits can be exploited easily for manipulating formation convergence and motion tendencies such as deformation (including expansion and shrinkage) and direction manipulation (including reversing and rotating) when flocking filings in accordance with the Reynolds' rules are considered. Numerical illustrations are sketched to show efficacy of the suggested control algorithms.