Persistently Exciting Online Feedback Optimization Controller with Minimal Perturbations

TL;DR

This paper introduces a novel Online Feedback Optimization controller that maintains persistent excitation for accurate gradient estimation without random perturbations, leading to faster convergence and improved resource allocation.

Contribution

It proposes a bilevel optimization-based OFO controller that minimizes perturbations while ensuring persistent excitation, eliminating the need for random inputs in feedback loops.

Findings

Achieved same profit as random perturbation OFO.

Attained 1.4% higher profit than non-perturbed OFO.

Validated in a resource allocation simulation.

Abstract

This paper develops a persistently exciting input generating Online Feedback Optimization (OFO) controller that estimates the sensitivity of a process ensuring minimal deviations from the descent direction while converging. This eliminates the need for random perturbations in feedback loop. The proposed controller is formulated as a bilevel optimization program, where a nonconvex full rank constraint is relaxed using linear constraints and penalization. The validation of the method is performed in a simulated scenario where multiple systems share a limited, costly resource for production optimization, simulating an oil and gas resource allocation problem. The method allows for less input perturbations while accurately estimating gradients, allowing faster convergence when the gradients are unknown. In the case study, the proposed method achieved the same profit compared to an OFO controller with random input perturbations, and $1.4\%$ higher profit compared to an OFO controller without input perturbations.