A Discrete-Time Adaptive ILC for Systems with Random Initial Condition and Iteration-Varying Trajectory

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A discrete-time adaptive ILC scheme is presented for systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new AILC can incorporate a recursive Least-Squares 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. An extension of the new AILC is also developed by using nonlinear data weighting to systems without assuming any growth conditions on the nonlinearity.