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.

Publication:

-    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 66, 10 (2021)

Authors:

-    Siyu Xie (Department of Electrical and Computer Engineering, Wayne State University)

-    Yaqi Zhang (Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences & School of Mathematical Science, University of Chinese Academy of Sciences)

-    Lei Guo (Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences & School of Mathematical Science, University of Chinese Academy of Sciences)