Robust ILC with iteration-varying initial state shifts: A 2D approach

This paper deals with the problem of varying initial state shifts in continuous-time iterative learning control (ILC) by employing the two-dimensional (2D) analysis approach. Two PD-type ILC algorithms are considered based on an average operator, where the second one is combined with an initial rectifying action. For both ILC algorithms, 2D Roesser systems are applied to develop sufficient conditions to guarantee their convergence. It is shown that the ILC processes converge with the increasing of iteration, and the converged tracking error can be formulated in terms of the mean of the initial output error and the learning parameters. Numerical simulations are given to illustrate that both ILC algorithms are robust against varying initial state errors, and the second one can achieve uniform convergence over any specified time interval with good learning transients.