A batch-to-batch optimal iterative learning control(ILC)strategy for the tracking control of product quality in batch processes is presented.The linear time-varying perturbation(LTVP)model is built for product quality around the nominal trajectories.To address problems of model-plant mismatches

model prediction errors in the previous batch run are added to the model predictions for the current batch run.Then tracking error transition models can be built

and the ILC law with direct error feedback is explicitly obtained.A rigorous theorem is proposed

to prove the convergence of tracking error under ILC.The proposed methodology is illustrated on a typical batch reactor and the results show that the performance of trajectory tracking is gradually improved by the ILC.