Diffusion-Based Distributed Parameter Estimation Through Directed Graphs With Switching Topology: Application of Dynamic Regressor Extension and Mixing

Abstract

In this article, we consider the problem of discrete-time, diffusion-based distributed parameter estimation with the agents connected via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">directed</i> graphs with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">switching</i> topologies and a self loop at each node. We show that, by incorporating the recently introduced dynamic regressor extension and mixing procedure to a classical gradient-descent algorithm, improved convergence properties can be achieved. In particular, it is shown that with this modification sufficient conditions for global convergence of all the estimators is that one of the sensors receives enough information to generate a consistent estimate and that this sensor is “well-connected.” The main feature of this result is that the excitation condition imposed on this distinguished sensor is strictly weaker than the classical persistent excitation requirement. The connectivity assumption is also very mild, requiring only that the union of the edges of all connectivity graphs over any time interval with an arbitrary but fixed length contains a spanning tree rooted at the information-rich node. In the case of nonswitching topologies, this assumption is satisfied by strongly connected graphs, and not only by them.