Optimal iterative learning control under varying iteration lengths with input saturation

This article is concerned with optimized iterative learning control of linear time-invariant systems against input saturation and varying iteration length. The varying length is described by a stochastic form. The corresponding iteration output is modified by the combination of the real iteration output and the desired one with the varying consideration. To optimize the tracking error, the constraint caused by input saturation is transformed to an unconstraint structure by a barrier method. Newton's method based optimal control law is adopted to minimize the quadratic index related to a modified tracking error. Rigorous theoretical derivations are presented to guarantee the convergence of tracking errors. An example is provided to confirm the validity of the proposed approach.