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arXiv · 1309.6613

Continuous-time Proportional-Integral Distributed Optimization for Networked Systems

Greg Droge·Hiroaki Kawashima·Magnus Egerstedt
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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.

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Greg Droge, Hiroaki Kawashima, Magnus Egerstedt. 2013-09-25. Continuous-time Proportional-Integral Distributed Optimization for Networked Systems. https://arxiv.org/abs/1309.6613

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