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Title: Asynchronous and Distributed Tracking of Time-Varying Fixed Points

Abstract

This paper develops an algorithmic framework for tracking fixed points of time-varying contraction mappings. Analytical results for the tracking error are established for the cases where: (i) the underlying contraction self-map changes at each step of the algorithm; (ii) only an imperfect information of the map is available; and, (iii) the algorithm is implemented in a distributed fashion, with communication delays and packet drops leading to asynchronous algorithmic updates. The analytical results are applicable to several classes of problems, including time-varying contraction mappings emerging from online and asynchronous implementations of gradient-based methods for time-varying convex programs. In this domain, the proposed framework can also capture the operating principles of feedback-based online algorithms, where the online gradient steps are suitably modified to accommodate actionable feedback from an underlying physical or logical network. Examples of applications and illustrative numerical results are provided.

Authors:
 [1];  [2]
  1. National Renewable Energy Laboratory (NREL), Golden, CO (United States)
  2. University of Colorado
Publication Date:
Research Org.:
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Sponsoring Org.:
USDOE National Renewable Energy Laboratory (NREL), Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1501652
Report Number(s):
NREL/CP-5D00-73480
DOE Contract Number:  
AC36-08GO28308
Resource Type:
Conference
Resource Relation:
Conference: Presented at the 2018 IEEE Conference on Decision and Control (CDC), 17-19 December 2018, Miami Beach, Florida
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; fixed points; time-varying contraction; tracking; asynchronous; distributed

Citation Formats

Bernstein, Andrey, and Dall'Anese, Emiliano. Asynchronous and Distributed Tracking of Time-Varying Fixed Points. United States: N. p., 2019. Web. doi:10.1109/CDC.2018.8619430.
Bernstein, Andrey, & Dall'Anese, Emiliano. Asynchronous and Distributed Tracking of Time-Varying Fixed Points. United States. doi:10.1109/CDC.2018.8619430.
Bernstein, Andrey, and Dall'Anese, Emiliano. Mon . "Asynchronous and Distributed Tracking of Time-Varying Fixed Points". United States. doi:10.1109/CDC.2018.8619430.
@article{osti_1501652,
title = {Asynchronous and Distributed Tracking of Time-Varying Fixed Points},
author = {Bernstein, Andrey and Dall'Anese, Emiliano},
abstractNote = {This paper develops an algorithmic framework for tracking fixed points of time-varying contraction mappings. Analytical results for the tracking error are established for the cases where: (i) the underlying contraction self-map changes at each step of the algorithm; (ii) only an imperfect information of the map is available; and, (iii) the algorithm is implemented in a distributed fashion, with communication delays and packet drops leading to asynchronous algorithmic updates. The analytical results are applicable to several classes of problems, including time-varying contraction mappings emerging from online and asynchronous implementations of gradient-based methods for time-varying convex programs. In this domain, the proposed framework can also capture the operating principles of feedback-based online algorithms, where the online gradient steps are suitably modified to accommodate actionable feedback from an underlying physical or logical network. Examples of applications and illustrative numerical results are provided.},
doi = {10.1109/CDC.2018.8619430},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {1}
}

Conference:
Other availability
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