  In this work we address the problem of performing a repetitive task when we
have uncertain observations and dynamics. We formulate this problem as an
iterative infinite horizon optimal control problem with output feedback.
Previously, this problem was solved for linear time-invariant (LTI) system for
the case when noisy full-state measurements are available using a robust
iterative learning control framework, which we refer to as robust
learning-based model predictive control (RL-MPC). However, this work does not
apply to the case when only noisy observations of part of the state are
available. This limits the applicability of current approaches in practice:
First, in practical applications we typically do not have access to the full
state. Second, uncertainties in the observations, when not accounted for, can
lead to instability and constraint violations. To overcome these limitations,
we propose a combination of RL-MPC with robust output feedback model predictive
control, named robust learning-based output feedback model predictive control
(RLO-MPC). We show recursive feasibility and stability, and prove theoretical
guarantees on the performance over iterations. We validate the proposed
approach with a numerical example in simulation and a quadrotor stabilization
task in experiments.
