Analysis of two robust learning control schemes in the presence of random iteration-varying noise

This paper deals with the design problem of robust iterative learning control (ILC), in the presence of noise that is varying randomly from iteration to iteration. Two ILC schemes are considered: one adopts the previous iteration tracking error (PITE) and the other adopts the current iteration tracking error (CITE), in the updating law. For both schemes, the convergence results are obtained by using a frequency-domain approach, and a comparison between them is presented from the viewpoints of the convergence condition, robustness against plant uncertainty, and delay compensation. It shows that sufficient conditions can be derived to bound the tracking error and make its expectation monotonically convergent in the sense of ℒ₂-norm, which work effectively with robustness for all admissible plant uncertainties. Furthermore, the sufficient conditions for both schemes can also be formulated in terms of two complementary functions, which do not depend on the delay time as well as the plant uncertainty and, thus, make them convenient to be checked and solved using the frequency-domain tools. Numerical simulations are included to illustrate the effectiveness of the two proposed ILC schemes.