  We propose a computationally efficient Learning Model Predictive Control
(LMPC) scheme for constrained optimal control of a class of nonlinear systems
where the state and input can be reconstructed using lifted outputs. For the
considered class of systems, we show how to use historical trajectory data
collected during iterative tasks to construct a convex value function
approximation along with a convex safe set in a lifted space of virtual
outputs. These constructions are iteratively updated with historical data and
used to synthesize predictive control policies. We show that the proposed
strategy guarantees recursive constraint satisfaction, asymptotic stability and
non-decreasing closed-loop performance at each policy update. Finally,
simulation results demonstrate the effectiveness of the proposed strategy on a
piecewise affine (PWA) system, kinematic unicycle and bilinear DC motor.
