Continuous-time Proportional-Integral Distributed Optimization for Networked Systems
Abstract
In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimization. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimization with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimization method. Furthermore, we establish convergence using Lyapunov stability techniques and utilizing properties from the network structure of the multi-agent system.
Cite
@article{arxiv.1309.6613,
title = {Continuous-time Proportional-Integral Distributed Optimization for Networked Systems},
author = {Greg Droge and Hiroaki Kawashima and Magnus Egerstedt},
journal= {arXiv preprint arXiv:1309.6613},
year = {2014}
}
Comments
23 Pages, submission to Journal of Control and Decision, under review. Takes comments from previous review process into account. Reasons for a continuous approach are given and minor technical details are remedied. Largest revision is reformatting for the Journal of Control and Decision