This work presents a controller with parameter estimation focused on non-linear, unknown and time-variant systems. The proposal consists of an on-line learning algorithm to estimate the system equations, and a controller that uses this information to stabilize the plant. Our approach is to combine a non-linear observer and a parameter estimator using sparse optimization techniques. The resulting algorithm operates in two stages: the learning stage, where unknown functions are learned on-line, and the execution stage, where the plant is controlled with pre-established objectives. The proposed algorithm can autonomously decide what is its current stage by using a learning metric. We have validated our algorithm using numerical simulation in a roto-magnet plant.