Muhammad, Abubakr (Univ. of Pennsylvania), Egerstedt, Magnus (Georgia Inst. of Tech.)

Control Using Higher Order Laplacians in Network Topologies

Scheduled for presentation during the Regular Session "Control of Mechanical Systems" (TuP07), Tuesday, July 25, 2006, 17:25−17:50, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 27, 2023

Abstract

This paper establishes the proper notation and precise interpretation for Laplacian flows on simplicial complexes. In particular, we have shown how to interpret these flows as time-varying discrete differential forms that converge to harmonic forms. The stability properties of the corresponding dynamical system are shown to be related to the topological structure of the underlying simplicial complex. Finally, we discuss the relevance of these results in the context of networked control and sensing.