Safe Feedback Optimization through Control Barrier Functions

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.

💡 Research Summary

Feedback optimization seeks to drive a dynamical system toward a steady‑state that solves a prescribed optimization problem, offering robustness to disturbances and model uncertainties compared with offline, feed‑forward approaches. While substantial progress has been made, most existing methods only guarantee input constraints or enforce state constraints asymptotically, leaving a critical gap: ensuring that state constraints are satisfied at all times during transients. This paper closes that gap by introducing a novel controller that merges two powerful ideas—Safe Gradient Flows (SGFs) and High‑Order Control Barrier Functions (HOCBFs)—to obtain a feedback‑optimization scheme that is both safe and stable.

Problem setting.
The plant is described by (\dot\xi = f(\xi,\nu)) with a globally exponentially stable equilibrium map (w(u)) for any constant input (u). The optimization problem is
\