Optimal selection of the forgetting matrix into an iterative learning control algorithm

A recursive optimal algorithm, based on minimizing the input error covariance matrix, is derived to generate the optimal forgetting matrix and the learning gain matrix of a P-type iterative learning control (ILC) for linear discrete-time varying systems with arbitrary relative degree. This note shows that a forgetting matrix is neither needed for boundedness of trajectories nor for output tracking. In particular, it is shown that, in the presence of random disturbances, the optimal forgetting matrix is zero for all learning iterations. In addition, the resultant optimal learning gain guarantees boundedness of trajectories as well as uniform output tracking in presence of measurement noise for arbitrary relative degree.