Adaptive Iterative Learning Control for Underactuated Systems with Unknown Input Distribution Matrices: Ensuring Input Continuity

This work investigates the adaptive iterative learning control (AILC) problem for a class of underactuated systems with unknown input distribution matrices. By introducing a newly designed control gain matrix, a novel AILC algorithm is proposed, which is able to deal with the unknown nonsquare control gain matrix effectively. Additionally, an auxiliary system is adopted to deal with the input saturation. The convergence of the proposed control algorithm is rigorously analyzed by using the composite energy function (CEF) method. The effectiveness is demonstrated through a numerical example.