  We present a sample-based Learning Model Predictive Controller (LMPC) for
constrained uncertain linear systems subject to bounded additive disturbances.
The proposed controller builds on earlier work on LMPC for deterministic
systems. First, we introduce the design of the safe set and value function used
to guarantee safety and performance improvement. Afterwards, we show how these
quantities can be approximated using noisy historical data. The effectiveness
of the proposed approach is demonstrated on a numerical example. We show that
the proposed LMPC is able to safely explore the state space and to iteratively
improve the worst-case closed-loop performance, while robustly satisfying state
and input constraints.
