Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition

In this work we present a discrete-time adaptive iterative learning control (AILC) scheme to deal with systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new adaptive ILC can incorporate a Recursive Least Squares (RLS) algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis.