In this paper, we present a learning-based adaptive method to solve the problem of robust trajectory tracking for electromagnetic actuators. We merge a nonlinear backstepping controller that ensures bounded input/bounded states stability, with a multi-variable extremum seeking model-free learning algorithm. The learning algorithm is used to estimate online the uncertain parameters of the model, in this sense, we propose a learning-based adaptive controller. We present a proof of stability of this learning-based nonlinear controller when considering uncertainties with linear parametrisation. The efficiency of this approach is shown on a numerical example.