Robust iterative learning control for linear discrete-time systems with initial state learning

This paper investigates a new sufficient robust convergence condition of iterative learning control with initial state learning in the presence of iteration-varying uncertainty for multivariable systems in the time domain. The uncertainty in system parameters may lead to divergence of the ILC algorithm. Moreover, in the basic ILC algorithm, the initial state is constant in each iteration and, consequently, always leads to a tracking error. Providing fixed learning gains over time and iteration is a significant achievement of this norm-based method. For this purpose, first, a new robust convergence condition is designed based on the iterative learning control with initial state learning algorithm, and in the next step, a semi-optimal solution is achieved for it by the imperialist competitive algorithm . Finally, the effectiveness of the proposed convergence scheme is evaluated through two numerical examples.