AILC for nonlinear systems with unknown time-varying control gain matrices

In this work, a novel adaptive iterative learning control (AILC) scheme is proposed for a class of uncertain multi-input multi-output (MIMO) systems, where the control gain matrices are both unknown and time-varying. In order to develop the AILC scheme without requiring the exact knowledge of the control gain matrix, a directional parameter is firstly introduced to indicate the control direction, which thus paves the way to the utilization of the Nussbaum gain technique. Furthermore, the parametric uncertainty and the unknown control gain matrix are transformed into a norm-based function, based on which both the feedback control law and the parametric updating law are established to ensure the perfect tracking performance of the system states along the iteration axis. The convergence of the tracking error is rigorously analyzed under the framework of the composite energy function (CEF). Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed AILC scheme.