  We introduce an autonomous system with closed-loop damping for first-order
convex optimization. While, to this day, optimal rates of convergence are
almost exclusively achieved by non-autonomous methods via open-loop damping
(e.g., Nesterov's algorithm), we show that our system, featuring a closed-loop
damping, exhibits a rate arbitrarily close to the optimal one. We do so by
coupling the damping and the speed of convergence of the system via a
well-chosen Lyapunov function. By discretizing our system we then derive an
algorithm and present numerical experiments supporting our theoretical
findings.
