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Nonconvex Distributed Feedback Optimization for Aggregative Cooperative Robotics

Guido Carnevale, Nicola Mimmo, Giuseppe Notarstefano

TL;DR

The paper introduces Aggregative Tracking Feedback, a distributed feedback optimization law for aggregative problems with nonlinear agent dynamics and nonconvex costs. By coupling a closed-loop gradient flow with consensus-based estimators, agents reconstruct global information and drive the network toward stationary points of the aggregative objective, with rigorous convergence guarantees under a two-timescale framework. The theoretical results are supported by a multi-robot surveillance case study demonstrating asymptotic convergence of optimality and global-consensus errors, as well as robustness to disturbances. This work advances distributed control by enabling fully decentralized optimization for tightly coupled, nonconvex aggregative problems in cooperative robotics. The proposed approach has potential implications for scalable coordination in multi-agent systems where global information is inaccessible or costly to centralized computation.

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.

Nonconvex Distributed Feedback Optimization for Aggregative Cooperative Robotics

TL;DR

The paper introduces Aggregative Tracking Feedback, a distributed feedback optimization law for aggregative problems with nonlinear agent dynamics and nonconvex costs. By coupling a closed-loop gradient flow with consensus-based estimators, agents reconstruct global information and drive the network toward stationary points of the aggregative objective, with rigorous convergence guarantees under a two-timescale framework. The theoretical results are supported by a multi-robot surveillance case study demonstrating asymptotic convergence of optimality and global-consensus errors, as well as robustness to disturbances. This work advances distributed control by enabling fully decentralized optimization for tightly coupled, nonconvex aggregative problems in cooperative robotics. The proposed approach has potential implications for scalable coordination in multi-agent systems where global information is inaccessible or costly to centralized computation.

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.
Paper Structure (12 sections, 4 theorems, 50 equations, 5 figures, 1 algorithm)

This paper contains 12 sections, 4 theorems, 50 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. Aggregative Tracking Feedback
  4. Closed-Loop System Analysis
  5. System Reformulation
  6. Preparatory Results
  7. Proof of Theorem \ref{['th:convergence']}
  8. Multi-robot Surveillance
  9. Conclusion
  10. Proof of Lemma \ref{['lemma:W']}
  11. Proof of Lemma \ref{['lemma:S']}
  12. Proof of Lemma \ref{['lemma:U']}

Key Result

Theorem 3.1

Consider eq:continuous_aggregative and let Assumptions ass:steady_state, ass:lipschitz, and ass:network hold. Then, there exist $\bar{\alpha}_1, \bar{\alpha}_2 > 0$ such that, for all $\textsc{col}(x_i(0),u_i(0),w_i(0),z_i(0)) \in \mathbb{R}^{n_i + m_i + 2d}$ such that $z_i = w_i = 0$ for all $i \in Further, given any $\bar{u} \in \mathbb{R}^{m}$ being an isolated stationary point and a local mini

Figures (5)

  • Figure 1: Block diagram describing \ref{['eq:continuous_aggregative']}.
  • Figure 2: Multi-robot surveillance: errors evolution.
  • Figure 3: Multi-robot surveillance: nonconvex scenario.
  • Figure 4: Multi-robot surveillance: strongly convex scenario.
  • Figure 5: Multi-robot surveillance: disturbed case.

Theorems & Definitions (6)

  • Theorem 3.1
  • Remark 3.2
  • Lemma 4.1
  • Lemma 4.2
  • Lemma 4.3
  • Remark 5.1