Passivity-Based Distributed Optimization with Communication Delays Using PI Consensus Algorithm

TL;DR

This paper introduces a passivity-based distributed optimization method that effectively manages communication delays using PI consensus algorithms, applicable to both constrained and unconstrained problems, demonstrated through a visual human localization application.

Contribution

It presents a novel passivity-based approach for distributed optimization with communication delays, extending to constrained problems with minimal additional complexity.

Findings

Effective handling of communication delays using scattering transformation.

Extension of the method to constrained optimization with a simple feedback addition.

Successful application to a visual human localization task.

Abstract

In this paper, we address a class of distributed optimization problems in the presence of inter-agent communication delays based on passivity. We first focus on unconstrained distributed optimization and provide a passivity-based perspective for distributed optimization algorithms. This perspective allows us to handle communication delays while using scattering transformation. Moreover, we extend the results to constrained distributed optimization, where it is shown that the problem is solved by just adding one more feedback loop of a passive system to the solution of the unconstrained ones. We also show that delays can be incorporated in the same way as the unconstrained problems. Finally, the algorithm is applied to a visual human localization problem using a pedestrian detection algorithm.