  This paper presents an iterative learning control (ILC) scheme for
continuously operated repetitive systems for which no initial condition reset
exists. To accomplish this, we develop a lifted system representation that
accounts for the effect of the initial conditions on dynamics and projects the
dynamics over multiple future iterations. Additionally, we develop an economic
cost function and update law that considers the performance over multiple
iterations in the future, thus allowing for the prediction horizon to be larger
than just the next iteration. Convergence of the iteration varying initial
condition and applied input are proven and demonstrated using a simulated
servo-positioning system test case.
