  This paper presents a stochastic model predictive controller (SMPC) for
linear time-invariant systems in the presence of additive disturbances. The
distribution of the disturbance is unknown and is assumed to have a bounded
support. A sample-based strategy is used to compute sets of disturbance
sequences necessary for robustifying the state chance constraints. These sets
are constructed offline using samples of the disturbance extracted from its
support. For online MPC implementation, we propose a novel reformulation
strategy of the chance constraints, where the constraint tightening is computed
by adjusting the offline computed sets based on the previously realized
disturbances along the trajectory. The proposed MPC is recursive feasible and
can lower conservatism over existing SMPC approaches at the cost of higher
offline computational time. Numerical simulations demonstrate the effectiveness
of the proposed approach.
