Nonlinear backstepping learning-based adaptive control of electromagnetic actuators with proof of stability

In this paper we present a learning-based adaptive method to solve the problem of robust trajectory tracking for electromagnetic actuators. We propose a learning-based adaptive controller; we merge together a nonlinear backstepping controller that ensures bounded input/bounded states stability, with a model-free multiparameter extremum seeking to estimate online the uncertain parameters of the system. We present a proof of stability of this learning-based nonlinear controller. We show the efficiency of this approach on a numerical example.