We present in this paper our preliminary results on the problem of learning-based adaptive trajectory tracking control for electromagnetic actuators. First, we develop a nominal nonlinear back stepping controller that stabilizes the tracking errors asymptotically and globally. Second, we robustify the nominal controller using a model-free learning technique, namely, multiparameter extremum seeking, to estimate the uncertain model parameters. In this sense we are proposing to solve an adaptive control problem with model-free learning based algorithms. We show the performance of the proposed controller on a numerical example.