  We propose an iterative approach for designing Robust Learning Model
Predictive Control (LMPC) policies for a class of nonlinear systems with
additive, unmodelled dynamics. The nominal dynamics are assumed to be
difference flat, i.e., the state and input can be reconstructed using flat
output sequences. For the considered class of systems, we synthesize Robust MPC
policies and show how to use historical trajectory data collected during
iterative tasks to 1) obtain bounds on the unmodelled dynamics and 2) construct
a convex value function approximation along with a convex safe set in the space
of output sequences for designing terminal components in the Robust MPC design.
We show that the proposed strategy guarantees robust constraint satisfaction,
asymptotic convergence to a desired subset of the state space, and
non-decreasing closed-loop performance at each policy update. Finally,
simulation results demonstrate the effectiveness of the proposed strategy on a
minimum time control problem using a constrained nonlinear and uncertain
vehicle model.
