Robust learning model predictive control for iterative tasks: Learning from experience

We present a Robust Learning Model Predictive Controller (RLMPC) for constrained uncertain systems performing iterative tasks. The proposed controller builds on earlier work of Learning Model Predictive Control (LMPC) for deterministic systems. The main idea behind RLMPC is to collect data from previous iterations and use it to estimate the current value function and build a robust safe set. We demonstrate that the proposed RLMPC algorithm is able to iteratively improve its control performance and robustly satisfy system constraints. The efficacy and limitations of the proposed RLMPC approach are illustrated on a numerical example.