  This work introduces a stochastic model predictive control scheme for dynamic
chance constraints. We consider linear discrete-time systems affected by
unbounded additive stochastic disturbance. To synthesize an optimal controller,
we solve two subsequent stochastic optimization problems. The first problem
concerns finding the maximal feasible probabilities of the dynamic chance
constraints. After obtaining the probabilities, the second problem concerns
finding an optimal controller using stochastic model predictive control. We
solve both stochastic optimization problems by reformulating them into
deterministic ones using probabilistic reachable tubes and constraint
tightening. We prove that the developed algorithm is recursively feasible and
yields closed-loop satisfaction of the dynamic chance constraints. In addition,
we will introduce a novel implementation using zonotopes to describe the
tightening analytically. Finally, we will end with an example illustrating the
method's benefits.
