Decentralized Cohesive Response During Transitions for Higher-Order Agents under Network Delays

Cohesion in networks during transitions from one consensus value to another, i.e., the ability of agents to respond in a similar manner during the transition, can be as important as achieving the new consensus value. Existing decentralized network control strategies mainly concern with the convergence speed to the final consensus value. However, even with increased convergence speed, the level of cohesion loss during transitions can be large. This loss of cohesion during transition (and tracking of varying consensus values) can be alleviated using a recently developed delayed self reinforcement (DSR) approach. However, the current DSR-based approach assumes ideal conditions with agents having instant access to neighbor information—without network delays arising during sensing or communication between neighbors, as well as computation of control actions of each agent, which can cause instability. The main contributions of this article are to use the Rouchè’s theorem to 1) prove the stability of the DSR approach if the network delay is not too large; and 2) compute an estimate of the acceptable network delay margin (DM) for stability. Additionally, a simulation example is used to illustrate the estimation approach for network DMs with DSR, and show that cohesion is maintained with DSR even with network delays when compared to the case without DSR.