  We propose a safe approximation to joint chance-constrained programming where
the constraint functions are additively dependent on a normally-distributed
random vector. The approximation is analytical, meaning that it requires
neither numerical integrations nor sampling-based probability approximations.
Under mild assumptions, the approximation is a standard nonlinear program. We
compare this new safe approximation to another analytical safe approximation
for joint chance-constrained programming based on Boole's inequality through
two examples representing the constrained control of linear Gaussian-Markov
models. It is shown that our proposed safe approximation has a lower degree of
conservatism compared to the one based on Boole's inequality.
