  We present a robust adaptive model predictive control (MPC) framework for
nonlinear continuous-time systems with bounded parametric uncertainty and
additive disturbance. We utilize general control contraction metrics (CCMs) to
parameterize a homothetic tube around a nominal prediction that contains all
uncertain trajectories. Furthermore, we incorporate model adaptation using
set-membership estimation. As a result, the proposed MPC formulation is
applicable to a large class of nonlinear systems, reduces conservatism during
online operation, and guarantees robust constraint satisfaction and convergence
to a neighborhood of the desired setpoint. One of the main technical
contributions is the derivation of corresponding tube dynamics based on CCMs
that account for the state and input dependent nature of the model mismatch.
Furthermore, we online optimize over the nominal parameter, which enables
general set-membership updates for the parametric uncertainty in the MPC.
Benefits of the proposed homothetic tube MPC and online adaptation are
demonstrated using a numerical example involving a planar quadrotor.
