Pulse compensation for PD-type iterative learning control against initial state shift

The rectangular pulse function is adopted to incorporate feed-forward compensation for various proportional-derivative-type iterative learning control updating laws applied to a class of linear time-invariant systems with initial state shift. The objective of pulse compensation is to suppress the tracking discrepancy incurred by initial state shift. By means of the generalised Young inequality of the convolution integral, the tracking performance of the pulse-based learning updating laws is analysed and the suppressive effect of the pulse compensation is evaluated by measuring the tracking error in the sense of Lebesgue-p norm. The derivation clarifies that the upper bound of the asymptotical tracking error can be improved by tuning the compensation gain properly though it is determined not only by the proportional and derivative learning gains but also by the system state, input and output matrices as well. Numerical simulations show that pulse compensation can effectively suppress the tracking error caused by initial state shift.