Observer-based iterative learning control with varying iteration lengths and alignment condition

Observer-based iterative learning control is developed in this paper to meet nonlinear systems with alignment condition and varying iteration lengths. Alignment condition is treated by a modified reference trajectory to achieve spatial closed-loop. Virtual forms of estimation error and tracking error are provided to handle varying iteration lengths. An adaptive observer based controller is constructed in terms of two tracking error feedback and three compensation parts for reference trajectory, state estimation and parameter estimation. Convergence of the errors is guaranteed in the framework of the composite energy function. Finally, a comparative simulation is presented to demonstrate the advantage of the proposed algorithm.