On Finite-Iteration Convergence of Iterative Learning Control

In this paper, a new problem of finite-iteration convergence of iterative learning control is discussed for a linear time-varying system. Considering a PD-type learning law, the finite-iteration convergence is shown by introducing two-dimensional system theory under some assumptions. By solving a set of linear matrix inequalities, the two learning gains of the control law can be updated in real time to ensure that the tracking error converges to an arbitrarily specified bound within finite iterative operations. Simulation study illustrates the correctness of the theoretical results.