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

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. With the help of the scattering transformation, this perspective allows us to handle arbitrary and unknown constant communication delays in the distributed optimization problem. Moreover, we extend the results to constrained distributed optimization. Finally, the algorithm is applied to a visual human localization problem using a pedestrian detection algorithm.