Iterative Learning Predictive Control for Constrained Uncertain Systems

Abstract: Iterative learning control (ILC) improves the performance of a repetitive system by learning from previous trials. ILC can be combined with Model Predictive Control (MPC) to mitigate non-repetitive disturbances, thus improving overall system performance. However, existing approaches either assume perfect model knowledge or fail to actively learn system uncertainties, leading to conservativeness. To address these limitations we propose a binary mixed-integer ILC scheme, combined with a convex MPC scheme, that ensures robust constraint satisfaction, non-increasing nominal cost, and convergence to optimal performance. Our scheme is designed for uncertain nonlinear systems subject to both bounded additive stochastic noise and additive uncertain components. We showcase the benefits of our scheme in simulation.