We introduce Learning-Augmented Control (LAC), an approach that integrates untrusted machine learning predictions into the control of constrained, nonlinear dynamical systems. LAC is designed to achieve the "best-of-both-worlds" guarantees, i.e, near-optimal performance when predictions are accurate, and robust, safe performance when they are not. The core of our approach is a delayed confidence learning procedure that optimizes a confidence parameter online, adaptively balancing between ML and nominal predictions. We establish formal competitive ratio bounds for general nonlinear systems under standard MPC regularity assumptions. For the linear quadratic case, we derive a competitive ratio bound that is provably tight, thereby characterizing the fundamental limits of this learning-augmented approach. The effectiveness of LAC is demonstrated in numerical studies, where it maintains stability and outperforms standard methods under adversarial prediction errors.