ℒ1 adaptive control in an iterative learning control framework: Stability, robustness and design trade-offs

This paper introduces a modified robust iterative control framework with ℒ₁ adaptive feedback for single-input single-output (SISO) linear time invariant (LTI) systems with iteration varying constant parametric uncertainties. The adaptive loop compensates for nonrepetitive effects (exogenous disturbances and/or uncertainties) and ensures that the plant, as seen from the ILC input, is sufficiently close to its nominal value for performance improvement through learning. The ℒ₁ controller is reformulated to accommodate the feedforward input, resulting in an adaptation that considers changes in system response due to learning. A rigorous stability analysis is presented. Performance and trade-offs are evaluated via simulation.