The Gradient Tracking Is a Distributed Integral Action

• 成果类型: Article
• 署名作者: Notarnicola, Ivano; Bin, Michelangelo; Marconi, Lorenzo; Notarstefano, Giuseppe
• 署名单位: University of Bologna
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3248487
• 发表日期: 2023
• 页码: 7911-7918
• 关键词: Control for optimization; distributed optimization; gradient tracking; integral control

摘要

We revisit the recent gradient tracking algorithm for distributed consensus optimization from a control theoretic viewpoint. We show that the algorithm can be constructed by solving a servomechanism control problem stemming from the distributed implementation of a centralized gradient method. Moreover, we show that, if expressed in proper coordinates, the gradient tracking embeds an integral action fed by a signal related to the consensus error. Finally, we provide an alternative convergence analysis based on Lyapunov arguments that also proves exponential asymptotic stability of the optimal equilibrium.