  We consider the problem of optimally controlling stochastic, Markovian
systems subject to joint chance constraints over a finite-time horizon. For
such problems, standard Dynamic Programming is inapplicable due to the time
correlation of the joint chance constraints, which calls for non-Markovian, and
possibly stochastic, policies. Hence, despite the popularity of this problem,
solution approaches capable of providing provably-optimal and easy-to-compute
policies are still missing. We fill this gap by introducing an augmented binary
state to the system dynamics, allowing us to characterize the optimal policies
and propose a Dynamic Programming based solution method. Our analysis provides
a deep insight into the impact of joint chance constraints on the optimal
control policies.
