  A robust adaptive model predictive control (MPC) algorithm is presented for
linear, time invariant systems with unknown dynamics and subject to bounded
measurement noise. The system is characterized by an impulse response model,
which is assumed to lie within a bounded set called the feasible system set.
Online set-membership identification is used to reduce uncertainty in the
impulse response. In the MPC scheme, robust constraints are enforced to ensure
constraint satisfaction for all the models in the feasible set. The performance
objective is formulated as a worst-case cost with respect to the modeling
uncertainties. That is, at each time step an optimization problem is solved in
which the control input is optimized for the worst-case plant in the
uncertainty set. The performance of the proposed algorithm is compared to an
adaptive MPC algorithm from the literature using Monte-Carlo simulations.
