  This paper is concerned with solving chance-constrained finite-horizon
optimal control problems, with a particular focus on the recursive feasibility
issue of stochastic model predictive control (SMPC) in terms of mission-wide
probability of safety (MWPS). MWPS assesses the probability that the entire
state trajectory lies within the constraint set, and the objective of the SMPC
controller is to ensure that it is no less than a threshold value. This differs
from classic SMPC where the probability that the state lies in the constraint
set is enforced independently at each time instant. Unlike robust MPC, where
strict recursive feasibility is satisfied by assuming that the uncertainty is
supported by a compact set, the proposed concept of recursive feasibility for
MWPS is based on the notion of remaining MWPSs, which is conserved in the
expected value sense. We demonstrate the idea of mission-wide SMPC in the
linear SMPC case by deploying a scenario-based algorithm.
