Iterative learning control of a class of complex-valued systems described by Schrödinger equation

In this paper, boundary tracking control for a class of complex-valued systems described by Schrödinger equation (SE) is solved by using iterative learning control (ILC). The control is imposed on the boundary
$x=1$
. Since SE is a complex-valued, this leads to transforming the original equation into two coupled real-valued equations at first. Moreover, a complex P-type ILC algorithm is designed and the convergence analysis is derived rigorously based on the contraction mapping methodology. The result of this paper show the actual output of the system will converge to the given desired output as the number of iterations tends to infinity under some given conditions.