  This paper is concerned with model predictive control (MPC) of discrete-time
linear systems subject to bounded additive disturbance and mixed constraints on
the state and input, whereas the true disturbance set is unknown. Unlike most
existing work on robust MPC, we propose an algorithm incorporating online
learning that builds on prior knowledge of the disturbance, i.e., a known but
conservative disturbance set. We approximate the true disturbance set at each
time step with a parameterised set, which is referred to as a quantified
disturbance set, using disturbance realisations. A key novelty is that the
parameterisation of these quantified disturbance sets enjoys desirable
properties such that the quantified disturbance set and its corresponding rigid
tube bounding disturbance propagation can be efficiently updated online. We
provide statistical gaps between the true and quantified disturbance sets,
based on which, probabilistic recursive feasibility of MPC optimisation
problems is discussed. Numerical simulations are provided to demonstrate the
effectiveness of our proposed algorithm and compare with conventional robust
MPC algorithms.
