Iterative learning control for linear discrete-time systems with high relative degree under initial state vibration

For linear discrete-time multiple-input-multiple-output (MIMO) systems with high relative degree, this study presents three average operator-based iterative learning control (ILC) algorithms to investigate the effect of initial state vibration on ILC tracking error. The proposed ILC laws include an initial rectifying action against initial state vibration at certain time points, and pursue the reference trajectory tracking beyond the initial time points. It is proved that, when the proposed ILC laws are applied to linear discrete-time MIMO systems with high relative degree, the effect of the initial state vibration on ILC tracking error beyond the initial time points can be exactly decided. Moreover, the ILC tracking error beyond the initial time points can be driven to zero against a progressive fixed initial state error. Numerical examples are used to illustrate the effectiveness of the proposed ILC laws.