Online Feedback Optimization for Monotone Systems without Timescale Separation

TL;DR

This paper demonstrates that Online Feedback Optimization can achieve optimal steady-states in monotone systems without requiring the controller to operate on a slower timescale than the plant, enhancing responsiveness.

Contribution

It relaxes the timescale separation assumption for OFO in monotone systems, providing conditions for global convergence based solely on steady-state behavior.

Findings

OFO achieves optimal steady-state without timescale separation.

Convergence conditions depend only on steady-state behavior.

Results apply to a broad class of monotone systems.

Abstract

Online Feedback Optimization (OFO) steers a dynamical plant to a cost-efficient steady-state, only relying on input-output sensitivity information, rather than on a full plant model. Unlike traditional feedforward approaches, OFO leverages real-time measurements from the plant, thereby inheriting the robustness and adaptability of feedback control. Unfortunately, existing theoretical guarantees for OFO assume that the controller operates on a slower timescale than the plant, which can affect responsiveness and transient performance. In this paper, we focus on relaxing this ``timescale separation'' assumption. Specifically, we consider the class of monotone systems, and we prove that OFO can achieve an optimal operating point, regardless of the time constants of controller and plant. By leveraging a small gain theorem for monotone systems, we derive several sufficient conditions for global convergence. Notably, these conditions depend only on the steady-state behavior of the plant, and they are entirely independent of the transient dynamics.