# Stochastic Online Feedback Optimization for Networks of Non-Compliant Agents

## TL;DR

This paper extends online feedback optimization to stochastic settings with non-compliant agents, providing theoretical error bounds and demonstrating applicability to power systems.

## Contribution

It introduces a stochastic OFO framework accommodating non-compliant agents, with proven mean-square error bounds and practical application to power networks.

## Key findings

- Derived mean-square error bounds for the stochastic OFO algorithm.
- Validated the approach through application to power system scenarios.
- Demonstrated robustness of the method with non-compliant agents.

## Abstract

In several applications of online optimization to networked systems such as power grids and robotic networks, information about the system model and its disturbances is not generally available. Within the optimization community, increasing interest has been devoted to the framework of online feedback optimization (OFO), which aims to address these challenges by leveraging real-time input-output measurements to empower online optimization. We extend the OFO framework to a stochastic setting, allowing the subsystems comprising the network (the $\textit{agents}$) to be $\textit{non-compliant}$. This means that the actual control input implemented by the agents is a random variable depending upon the control setpoint generated by the OFO algorithm. Mean-square error bounds are obtained for the general algorithm and the theory is illustrated in application to power systems.