Brief paper repetitive learning control for triangular systems with unknown control directions

A backstepping repetitive learning control method is proposed for a class of high-order non-linear systems with triangular structure with unknown control coefficients. The Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control directions. A differential-difference repetitive control law is presented to avoid the difficulties encountered in the derivation of the fictitious control. It is proved that the output of controlled system converges to the desired trajectory asymptotically along the iterative learning axis through repetitive learning. Simulation is carried out to show the validity of the proposed control method.