Passivity As a Design Tool for Cooperative Control

Abstract

In this chapter, we formulate a coordination problem that is applicable to formation stabilization and group agreement as special cases, and present a class of feedback laws that solve this problem with local information. A key observation is that bidirectional communication gives rise to Structure 4 in Section 1.5, which guarantees that the resulting feedback loop will inherit the passivity properties of its components. By exploiting this structure, we develop a design method which results in a broad class of feedback laws that achieve passivity and, thus, stability of the interconnected system. The passivity approach also leads to a systematic construction of a Lyapunov function in the form of a sum of storage functions for the subsystems. As detailed in this chapter, several existing feedback rules for formation stability and group agreement become special cases in the passivity framework.