  We propose an Adaptive MPC framework for uncertain linear systems to achieve
robust satisfaction of state and input constraints. The uncertainty in the
system is assumed additive, state dependent, and globally Lipschitz with a
known Lipschitz constant. We use a non-parametric technique for online
identification of the system uncertainty by approximating its graph via
envelopes defined by quadratic constraints. At any given time, by solving a set
of convex optimization problems, the MPC controller guarantees robust
constraint satisfaction for the closed loop system for all possible values of
system uncertainty modeled by the envelope. The uncertainty envelope is refined
with data using Set Membership Methods. We highlight the efficacy of the
proposed framework via a detailed numerical example.
