Error Corrected References for Accelerated Convergence of Low Gain Norm Optimal Iterative Learning Control

To reduce the need for high gains (reduced control weighting) for fast convergence in norm optimal iterative learning control (NOILC), this article presents a simple data-driven mechanism for accelerating the convergence of low gain feedback NOILC controllers. The method uses a modification to the reference signal on each NOILC iteration using the measured tracking error from the previous iteration. The basic algorithm is equivalent to a gradient iteration combined with an NOILC iteration. The choice of design parameters is interpreted in terms of the spectrum of the error update operator and the systematic annihilation of spectral components of the error signal. The methods apply widely, including continuous and discrete-time end point, intermediate point, and signal tracking. The effects of parameter choice are revealed using examples. A robustness analysis is presented and illustrated by frequency-domain robustness conditions for multi-input, multi-output discrete-time tracking, and robustness conditions for end-point problems for state-space systems. Finally, the algorithm is extended to embed a number of gradient iterations within a single NOILC iteration. This makes possible the systematic manipulation of the spectrum, providing additional acceleration capabilities with the theoretical possibility of arbitrary fast convergence.