Passivity as a Design Tool for Group Coordination

TLDR

The paper aims to steer the differences between group members’ outputs into a prescribed compact set and introduces a passivity‑based design framework that generalizes existing formation and agreement controllers. The authors propose locally implementable feedback rules based on passivity, analyze their robustness under time‑varying communication topologies using a persistency‑of‑excitation condition, and construct a Lurie‑type Lyapunov function for the closed loop. With bidirectional information flow the closed‑loop system acquires a special interconnection structure inheriting component passivity, and the passivity approach yields greater design flexibility and a systematic Lyapunov function.

Abstract

We pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set. To stabilize this set we study a class of feedback rules that are implementable with local information available to each member. When the information flow between neighboring members is bidirectional, we show that the closed-loop system exhibits a special interconnection structure which inherits the passivity properties of its components. By exploiting this structure we develop a passivity-based design framework, which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature. The passivity approach offers additional design flexibility compared to these special cases, and systematically constructs a Lurie-type Lyapunov function for the closed-loop system. We further study the robustness of these feedback laws in the presence of a time-varying communication topology, and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense.