Output feedback adaptive iterative learning control for nonlinear discrete-time systems with unknown control directions

An adaptive iterative learning control method is developed for a class of high-order nonlinear output feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. The n-step ahead predictor approach is employed to estimate the future outputs. The discrete Nussbaum gain method is incorporated into the control design to deal with the lack of a priori knowledge of the control directions. The proposed control algorithm guarantees that the tracking error converges to zero asymptotically along the iterative learning axis except for the beginning outputs affected by the random initial conditions with all the signals in the controlled system bounded. A numerical simulation is carried out to demonstrate the effectiveness of the proposed control laws.