Nonconvex Distributed Feedback Optimization for Aggregative Cooperative Robotics

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. This research was partially supported by the projects OPT4SMART n. 638992 funded by the European Research Council and "Distributed Optimization for Cooperative Machine Learning in Complex Networks" n. PGR10067 funded by Ministero degli Affari Esteri e della Cooperazione Internazionale.

Distributed Real-Time Feedback Optimization for Renewable Energy Sources and Vehicle-to-Grid Power Compensation of Electric Vehicle Chargers in Distribution Systems

“…FO uses the system output measurements to drive the equilibrium point of the system to the solution of a predefined optimization problem. It has been applied in various areas such as robotics control [32,33], transmission and distribution systems [25][26][27][28][29][30][31] and microgrid control [34][35][36]. This paper applies FO in the distribution system to optimally control EV chargers and RESs.…”

“…As a result, it is robust to model mismatch and has a low computational burden. FO has been applied in robotics control [32,33], transmission and distribution systems [25][26][27][28][29][30][31], and microgrid control [34][35][36].…”