Convergence of a Distributed Least Squares

• 成果类型: Article
• 署名作者: Xie, Siyu; Zhang, Yaqi; Guo, Lei
• 署名单位: Wayne State University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3047989
• 发表日期: 2021
• 页码: 4952-4959
• 关键词: convergence; estimation; Symmetric matrices; Stochastic processes; Task analysis; Complexity theory; Adaptive control; CONVERGENCE; cooperative excitation; diffusion strategies; distributed estimation; least squares (LS); Martingale Theory; regret

摘要

In this article, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is allowed to communicate with its neighbors. Our main task is to generalize the well-known theoretical results on the traditional LS to the current distributed case by establishing both the upper bound of the accumulated regrets of the adaptive predictor and the convergence of the distributed LS estimator, with the following key features compared with the existing literature on distributed estimation: First, our theory does not need the previously imposed independence, stationarity, or Gaussian property on the system signals, and hence is applicable to stochastic systems with feedback. Second, the cooperative excitation condition introduced and used in this article for the convergence of the distributed LS estimate is the weakest possible one, which shows that even if any individual sensor cannot estimate the unknown parameter by the traditional LS, the whole network can still fulfill the estimation task by the distributed LS.