  In this paper, we present a robust adaptive model predictive control (MPC)
scheme for linear systems subject to parametric uncertainty and additive
disturbances. The proposed approach provides a computationally efficient
formulation with theoretical guarantees (constraint satisfaction and
stability), while allowing for reduced conservatism and improved performance
due to online parameter adaptation. A moving window parameter set
identification is used to compute a fixed complexity parameter set based on
past data. Robust constraint satisfaction is achieved by using a
computationally efficient tube based robust MPC method. The predicted cost
function is based on a least mean squares point estimate, which ensures
finite-gain $\mathcal{L}_2$ stability of the closed loop. The overall algorithm
has a fixed (user specified) computational complexity. We illustrate the
applicability of the approach and the trade-off between conservatism and
computational complexity using a numerical example.
  This paper is an extended version of~[1], and contains additional details
regarding the theoretical proof of Theorem~1, the numerical example, and the
offline computations in Appendix~A--B.
