Nonconvex Distributed Feedback Optimization for Aggregative Cooperative Robotics

TL;DR

This paper introduces a novel distributed feedback control law for multi-agent systems to optimize a nonconvex aggregative cost function, ensuring convergence to a stationary point in cooperative robotics.

Contribution

It proposes Aggregative Tracking Feedback, a new distributed feedback law combining gradient flow and consensus dynamics for nonconvex aggregative optimization.

Findings

Proves convergence to stationary points using system theory tools.

Validates effectiveness through multi-robot surveillance simulations.

Abstract

Distributed aggregative optimization is a recently emerged framework in which the agents of a network want to minimize the sum of local objective functions, each one depending on the agent decision variable (e.g., the local position of a team of robots) and an aggregation of all the agents' variables (e.g., the team barycentre). In this paper, we address a distributed feedback optimization framework in which agents implement a local (distributed) policy to reach a steady-state minimizing an aggregative cost function. We propose Aggregative Tracking Feedback, i.e., a novel distributed feedback optimization law in which each agent combines a closed-loop gradient flow with a consensus-based dynamic compensator reconstructing the missing global information. By using tools from system theory, we prove that Aggregative Tracking Feedback steers the network to a stationary point of an aggregative optimization problem with (possibly) nonconvex objective function. The effectiveness of the proposed method is validated through numerical simulations on a multi-robot surveillance scenario.