Convergence rates and robustness of iterative learning control

It is desirable that iterative learning control algorithms have exponentially decreasing property, which yields robustness against the measurement noise, perturbation caused by initialization error, and so forth at each trial. In this paper, it is demonstrated that the algorithm with the property, however, cannot be constructed as far as the conventional design problem is concerned. In order to solve the problem, the design problem is modified via an introduction of digital controllers; the introduction brings the exponentially decreasing property in exchange for residuals caused necessarily by the digital-controller. To illustrate this, an algorithm based on the gradient method is presented and it is shown that the algorithm has robustness against disturbances. It is also proved that the residual approach 0 by the digital controller for a certain class of linear systems as the sampling period tends to 0.