Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints at all times. The difficulty in addressing it lies on mediating between the safety enforcement and the closed-loop stability, and ensuring the equivalence between closed-loop equilibria and the optimization problem's critical points. In this work, we present a feedback-optimization method that enforces state constraints at all times employing high-order control-barrier functions. We provide several results on the proposed controller dynamics, including well-posedness, safety guarantees, equivalence between equilibria and critical points, and local and global (in certain convex cases) asymptotic stability of optima. Various simulations illustrate our results.
@article{arxiv.2602.09928,
title = {Safe Feedback Optimization through Control Barrier Functions},
author = {Giannis Delimpaltadakis and Pol Mestres and Jorge Cortés and W. P. M. H. Heemels},
journal= {arXiv preprint arXiv:2602.09928},
year = {2026}
}