An analytical safe approximation to joint chance-constrained programming with additive Gaussian noises

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.